5.5 case 2 probability
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This document discusses probability concepts through examples involving dice rolls. It presents three probability questions: 1) finding the probability of rolling a sum greater than 9 on two dice, 2) finding the probability of rolling a sum that is a multiple of 3, and 3) finding the probability of rolling a sum that is divisible by 3 or 4. It defines the sample space of all possible dice roll outcomes. It then calculates the probabilities for each question by determining the number of favorable outcomes and dividing by the total number of outcomes. The probabilities calculated are 1/6, 1/3, and 5/9 respectively. Students are instructed to solve similar probability problems involving dice rolls.
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발표일: 18.3.12.
영유아기는 발달의 기초를 형성하는 시기로 이 시기에 발생하는 발달문제는 이후의 성장과 학습에도 심각한 문제를 초래할 수 있다. 따라서, 영유아의 발달 지연 또는 발달 장애의 조기 발견(early detection)과 조기 중재(early intervention)를 통해 이후의 문제를 최소화 하는 것이 중요하다.
아동 발달검사 방법으로서 부모보고형 방법이 널리 사용된다. 아동 발달 관련 질문에 부모가 답변함으로써 아동의 현 발달상황을 예측할 수 있다. 하지만, 한 부모의 보고에만 의존하는 경우 주관적인 의견이 많이 반영되거나 혼자만의 기억과 관찰에 의해서 답변되기 때문에 정확도가 낮아질 가능성이 있다. 이러한 문제를 해결하고자 아동발달에 관한 엄마와 아빠, 두 사람의 의견을 모으고 추가적으로 제3자(e.g., 어린이집 선생님, 친척 등)의 의견을 통해 보다 신뢰성있는 발달검사 결과를 얻기 위한 모바일 시스템 BebeCODE 를 제안하였다 [1].
또한, 발달 지연 특히 언어발달이 지연된 아동을 돕기위한 방법으로서 치료사의 직접 중재와 더불어 부모교육 을 통한 간접 중재 방법 역시 자주 사용된다. 이 과정에서 아동이 주도하는 대화법, 아동의 발화 혹은 반응을 기다려 주는 것, 천천히 말해주는 것과 같은 다양한 대화 전략들을 교육받게 되지만, 이러한 전략들을 실제 가정에서, 자신의 아동에게 직접 적용하는 것에 어려움을 겪는 경우가 많다. 따라서 부모-아동의 상호작용에 대해 실시간 피드백을 제공함으로써 가정에서 부모교육의 전략을 적용하는 데 도움을 주는 모바일 시스템 TalkLime 을 제안하였다 [2].
아동은 놀이를 통해서 대부분 학습하고 발달하게 된다. 다양한 놀이 자극을 위해서 엄마와 아빠와의 놀이가 모두 중요하지만, OECD 2015 통계에 의하면 대한민국의 아버지들의 육아 참여시간은 극도로 저조하다. 아버지들이 아동과의 놀이 과정에서 겪는 어려움을 분석하고 이에 도움을 주기 위한 모바일 시스템 PlayBetter을 제안하였다 [3].
박사과정 동안 수행한 모바일 시스템으로 아동의 발달을 보조할 수 있는 기회에 대해서 이야기하고 아동 발달 관련 시스템을 디자인할 때 특히 고려해야 할 점과 현재 진행중인 후속 연구에 대해서 소개 할 것이다.
[1] Seokwoo Song, Juho Kim, Bumsoo Kang, Wonjeong Park, John Kim.
“BebeCode: A System for Collaborative Child Development Tracking”
ACM International Conference on Human Factors in Computing Systems (CHI), 2018
[2] Seokwoo Song, Seungho Kim, John Kim, Wonjeong Park, Dongsun Yim.
“TalkLIME: Mobile System Intervention to Improve Parent-Child Interaction for Children with Language Delay”,
ACM international Joint Conference on Pervasive and Ubiquitous Computing (UBICOMP), 2016
[3] Seokwoo Song, Juho Kim, John Kim
“PlayBetter: A Phone-based Baby Play Support System for Childcare Bystander Parents”,
ACM International Conference on Human Factors in Computing Systems (CHI), 2017 Extended Abstract
Math138 lectures 3rd edition scoolbook
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一比一原版(UofS毕业证书)萨省大学毕业证如何办理
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（详情请加一下 文凭顾问+微信:95270640）欢迎咨询！的鬼地方父亲的家在高楼最底屋最下面很矮很黑是很不显眼的地下室父亲的家安在别人脚底下须绕过高楼旁边的垃圾堆下八个台阶才到父亲的家很狭小除了一张单人床和一张小方桌几乎没有多余的空间山娃一下子就联想起学校的男小便处山娃很想笑却怎么也笑不出来山娃很迷惑父亲的家除了一扇小铁门连窗户也没有墓穴一般阴森森有些骇人父亲的城也便成了山娃的城父亲的家也便成了山娃的家父亲让山娃呆在屋里做作业看电视最多只能在门口透透气间
一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理
毕业原版【微信:176555708】【(GWU,GW毕业证书)乔治·华盛顿大学毕业证】【微信:176555708】成绩单、外壳、offer、留信学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信176555708】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信176555708】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
Natural Language Processing (NLP), RAG and its applications .pptx
1. In the realm of Natural Language Processing (NLP), knowledge-intensive tasks such as question answering, fact verification, and open-domain dialogue generation require the integration of vast and up-to-date information. Traditional neural models, though powerful, struggle with encoding all necessary knowledge within their parameters, leading to limitations in generalization and scalability. The paper "Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks" introduces RAG (Retrieval-Augmented Generation), a novel framework that synergizes retrieval mechanisms with generative models, enhancing performance by dynamically incorporating external knowledge during inference.
Analysis insight about a Flyball dog competition team's performance
Insight of my analysis about a Flyball dog competition team's last year performance. Find more: https://github.com/rolandnagy-ds/flyball_race_analysis/tree/main
My burning issue is homelessness K.C.M.O.
My burning issue is homelessness in Kansas City, MO
To: Tom Tresser
From: Roger Warren
Predictably Improve Your B2B Tech Company's Performance by Leveraging Data
Harness the power of AI-backed reports, benchmarking and data analysis to predict trends and detect anomalies in your marketing efforts.
Peter Caputa, CEO at Databox, reveals how you can discover the strategies and tools to increase your growth rate (and margins!).
From metrics to track to data habits to pick up, enhance your reporting for powerful insights to improve your B2B tech company's marketing.
- - -
This is the webinar recording from the June 2024 HubSpot User Group (HUG) for B2B Technology USA.
Watch the video recording at https://youtu.be/5vjwGfPN9lw
Sign up for future HUG events at https://events.hubspot.com/b2b-technology-usa/
The Ipsos - AI - Monitor 2024 Report.pdf
According to Ipsos AI Monitor's 2024 report, 65% Indians said that products and services using AI have profoundly changed their daily life in the past 3-5 years.
Population Growth in Bataan: The effects of population growth around rural pl...
A population analysis specific to Bataan.
一比一原版(Bradford毕业证书)布拉德福德大学毕业证如何办理
原版定制【微信:41543339】【(Bradford毕业证书)布拉德福德大学毕业证】【微信:41543339】成绩单、外壳、offer、留信学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信41543339】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信41543339】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
一比一原版(UniSA毕业证书)南澳大学毕业证如何办理
原版定制【微信:41543339】【(UniSA毕业证书)南澳大学毕业证】【微信:41543339】成绩单、外壳、offer、留信学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信41543339】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信41543339】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理
毕业原版【微信:41543339】【(爱大毕业证书)爱丁堡大学毕业证】【微信:41543339】成绩单、外壳、offer、留信学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信41543339】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信41543339】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
一比一原版(Adelaide毕业证书)阿德莱德大学毕业证如何办理
原版定制【微信:41543339】【(Adelaide毕业证书)阿德莱德大学毕业证】【微信:41543339】成绩单、外壳、offer、留信学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信41543339】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信41543339】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
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→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...
This webinar will explore cutting-edge, less familiar but powerful experimentation methodologies which address well-known limitations of standard A/B Testing. Designed for data and product leaders, this session aims to inspire the embrace of innovative approaches and provide insights into the frontiers of experimentation!
办(uts毕业证书)悉尼科技大学毕业证学历证书原版一模一样
原版一模一样【微信：741003700 】【(uts毕业证书)悉尼科技大学毕业证学历证书】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
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留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
The Building Blocks of QuestDB, a Time Series Database
Talk Delivered at Valencia Codes Meetup 2024-06.
Traditionally, databases have treated timestamps just as another data type. However, when performing real-time analytics, timestamps should be first class citizens and we need rich time semantics to get the most out of our data. We also need to deal with ever growing datasets while keeping performant, which is as fun as it sounds.
It is no wonder time-series databases are now more popular than ever before. Join me in this session to learn about the internal architecture and building blocks of QuestDB, an open source time-series database designed for speed. We will also review a history of some of the changes we have gone over the past two years to deal with late and unordered data, non-blocking writes, read-replicas, or faster batch ingestion.
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5.5 case 2 probability
- 1. www.sanjivanimba.org.in Unit No.5. PROBABILITY Presented By: Dr. V. M. Tidake Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem) Dean, EDP & Associate Professor MBA 1 Sanjivani College of Engineering, Kopargaon Department of MBA www.sanjivanimba.org.in
- 2. www.sanjivanimba.org.in 302-DECISION SCIENCE Unit No.5. Probability 5.2 Case 2: Probability Presented By: Dr. V. M. Tidake Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem) Dean EDP & Associate Professor MBA 2 Sanjivani College of Engineering, Kopargaon Department of MBA www.sanjivanimba.org.in
- 3. www.sanjivanimba.org.in NETWORK ANALYSIS At the End of the Session Student will be able to understand- A. Case 2: Probability
- 4. www.sanjivanimba.org.in Probability A pair of dice is thrown. Find the probability of getting the sum- i) More than 9; ii) Multiple of 3 iii) Divisible by 3 or 4
- 5. www.sanjivanimba.org.in Probability The Sample Space in this case would be- {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}
- 6. www.sanjivanimba.org.in Probability • Total Number of possible outcomes, n= 36 i) Let A- Event that the sum is more than 9 i.e. the sum is 10 or 11 or 12 The favorable outcomes in this case are- (4,6) (5,5) (5,6) (6 4) (6 5) (6 6) Hence Probability is- • 𝑷 𝑩 = 𝒑 = 𝒎 𝒏 = 𝟔 𝟑𝟔 = 𝟏 𝟔
- 7. www.sanjivanimba.org.in Probability • Total Number of possible outcomes, n= 36 ii) Let B- Event that the sum is multiple of 3 The favorable outcomes in this case are- (1,2) (1,5) (2,1) (2,4) (3,3) (3,6) (4,2) (4,5) (5,1) (5,4) (6,3) (6,6) i.e. m=12 Hence Probability is- • 𝑷 𝑩 = 𝒑 = 𝒎 𝒏 = 𝟏𝟐 𝟑𝟔 = 𝟏 𝟑
- 8. www.sanjivanimba.org.in Probability iii) Let C- Event that the sum is multiple of 4 The favorable outcomes in this case are- (1,3) (2,2) (2,6) (3,1) (3,5) (4,4) (5,3) (6,2) (6,6) i.e. m=9 Hence Probability is- • 𝑷 𝑪 = 𝒑 = 𝒎 𝒏 = 𝟗 𝟑𝟔 = 𝟏 𝟒 Now Probability of Sum is divisible by both 3 & 4 is 𝑷 𝑩Ո𝑪 = 𝒑 = 𝒎 𝒏 = 𝟏 𝟑𝟔 Now the Probability that the sum is divisible by 3 or 4 is given as- 𝑃 𝐵Ս𝐶 = 𝑃 𝐵 + 𝑃 𝐶 − 𝑃 𝐵Ո𝐶 = 1 3 + 1 4 − 1 36 = 𝟓 𝟗
- 9. www.sanjivanimba.org.in EXERCISE Solve the Case 2 on Probability.
- 10. www.sanjivanimba.org.in For More Details Contact Dr. V M Tidake tidkevishal@gmail.com tidkevishalmba@sanjivani.org.in