INDEPENDENT AND DEPENDENT EVENTS
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This document discusses probability concepts through examples of independent and dependent events. It contains examples such as drawing balls from jars, tossing coins, solving problems by multiple students, selecting family members in interviews, defective light bulbs and food items, and cards from a deck. The document also provides probability questions involving sales promotions, people leaving a lift, accidentally dropped cards during shuffling, distributing balls in boxes, and a dice game between two people.
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Mutually exclusive events cannot occur at the same time. The probability of event A or B occurring is calculated as P(A) + P(B). Independent events do not influence each other, so P(A and B) = P(A) × P(B). Dependent events influence each other, so P(A and B) = P(A) × P(B after A). Examples are provided to demonstrate calculating probabilities for mutually exclusive, independent, and dependent events.
Independent and dependent events notes
1) Independent events are events where the outcome of one event does not affect the outcome of the next event. Dependent events are events where the outcome of the first event affects the probability of the outcome of the second event.
2) The probability of two independent events occurring is calculated by multiplying the individual probabilities. The probability of two dependent events occurring factors in how the first event affects the probability of the second.
3) Examples are provided to demonstrate calculating probabilities of independent and dependent events, such as spinning spinners or drawing marbles from a bag.
11.5 Independent and Dependent Events
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To find the probability of two independent events:
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mutually-exclusive-events.ppt
Mutually exclusive events cannot occur at the same time. The probability of event A or B occurring is calculated as P(A) + P(B). Independent events do not influence each other, so P(A and B) = P(A) × P(B). Dependent events influence each other, so P(A and B) = P(A) × P(B after A). Examples are provided to demonstrate calculating probabilities for mutually exclusive, independent, and dependent events.
Independent and dependent events notes
1) Independent events are events where the outcome of one event does not affect the outcome of the next event. Dependent events are events where the outcome of the first event affects the probability of the outcome of the second event.
2) The probability of two independent events occurring is calculated by multiplying the individual probabilities. The probability of two dependent events occurring factors in how the first event affects the probability of the second.
3) Examples are provided to demonstrate calculating probabilities of independent and dependent events, such as spinning spinners or drawing marbles from a bag.
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Identify whether events are independent or depdendent
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of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
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A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
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Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
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INDEPENDENT AND DEPENDENT EVENTS
- 2. • Determine whether the events are independent or dependent. (a)Akash draws a 4 from ten cards numbered 1 through 10. He replaces the card. Then Ramesh draws a 7. what is the probability of getting a 4 and a 7? (b)A jar contains 15 green balls and 5 red balls. If two balls are chosen at random one after another. What is the probability of getting two green balls?
- 3. • Suppose you have 10 green balls and 5 red balls. You take out one ball and then put it back. Then you take out another ball. What is the probability that you take out a green ball and then a red ball?
- 4. 1. Four coins are tossed. Find the probability that atleast one head turns up. 2. A problem in statistics is given to three sudents A, B, and C whose chances of solving it are ½ , 1/3 and ¼ respectively. What is the probability that (a) The problem is solved (b) At least two of them are able to solve (c) Exactly two of them are able to solve (d) Exactly one of them is able to solve (e) No one will solve the problem
- 5. 3. A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 1/7 and that of wife is 1/5. What is the probability that (a)Both of them will be selected (b)Only one of them will be selected (c) None of them will be selected
- 6. 4. A certain brand of light bulbs are defective 5% of the time. You randomly pick a pack of two such bulbs from the store. What is the probability that (a)exactly one bulb is defective? (b)At least one bulb is defective?
- 7. 5. A basket contain 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random, what is the probability that either both are apples or both are good? 6. Two cards are drawn from a pack of 52 cards. What is the probability that either both are red or both are kings?
- 8. Assignment 1. For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all coke bottles. You buy a six-pack. What is the probability that you win something (at least one bottle has a winner symbol)? 2. Five persons entered the lift on the ground floor of an 8th floor building. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. Find out the probability of all five persons leaving at different floors.
- 9. 3. In shuffling a pack of 52 playing cards, four are accidently dropped. Find the chance that the missing cards should be one from each suit. 4. Twelve balls are distributed among three boxes. What is the probability that the first box will contain 3 balls? 5. Two persons A and B throw a dice alternatively till one of them gets a ‘three’ and wins the game. Find their respective probabilities of winning, if A begins.