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# Different kinds of Probability

by Melissa velasco bsed 3

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### Different kinds of Probability

1. 1. SOUTHERN BICOL COLLEGES MASBATE CITY COMPILATION OF DIFFERENT KINDS OF PROBABILITY MELISSA G. VELASCO BSED-III (MAJOR IN MATHEMATICS) ENGR. MARIA ROMINA PRAC ANGUSTIA INSTRUCTOR TABLE OFCONTENTS
2. 2.  TABLE OF CONTENTS . . . . . . ii  HISTORY OF PROBABILITY . . . . . 1  PROBABILITY . . . . . . . 2  COMPLEMENTARY PROBABILITY . . . . 3  JOINT PROBABILITY . . . . . . 4-5  CONDITIONAL PROBABILITY . . . . . 6  INDEPENDENT PROBABILITY . . . . . 6  REPEATED TRIALS PROBABILITY . . . . 7 Ii
3. 3. HISTORY OF PROBABILITY A gambler’s dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Chevalier de Mere, a French nobleman had an interest about the gambling so he question the two famous mathematician about the scoring of the game. This problem and others posed by de Mere led to an exchange of letters between Pascal and Fermat in which the fundamental principles of probability theory were formulated for the first time. GAMING / GAMBLING The game consisted of throwing a pair of dice 24 times; the scoring was to decide whether or not to bet even money on the occurrence of at least one “double six” during the 24 throws. 1
4. 4. PROBABILITY Is the measure of how likely an event is to occur. FORMULA: P = 𝐸𝑉𝐸𝑁𝑇𝑆(𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑟𝑒𝑠𝑢𝑙𝑡 𝑜𝑓 𝑎 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡) 𝑂𝑈𝑇𝐶𝑂𝑀𝐸𝑆( 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑟𝑒𝑠𝑢𝑙𝑡 𝑜𝑓 𝑎 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡) EXAMPLE: What is the probability of getting head when flipping a coin? SOLUTION: 𝑃(ℎ𝑒𝑎𝑑) = 1 2 =0.05 =50% PROBABILITY NUMBER LINE Impossible unlikely equal chances likely certain 0 0.5 1 0% 50% 100% 2
5. 5. COMPLEMENTARY PROBABILITY  Is not of that event.  The sum of the probability is equal to 1. FORMULA: P(A) + P(B) = 1 or P(not A) =1 – P(A) EXAMPLE: A number is chosen at random from a set of whole numbers from 1 to 150. Calculate the probability that the chosen number is not a perfect square. SOLUTION: PS(1,4,9,16,25,36,49,64,81,100,121,144) P(not perfect square)=1 – P(perfect square) = 150 150 - 12 150 = 138 150 = 23 25 = 0.92 or 92% 3
6. 6. JOINT PROBABILITY Is the likelihood of more than one event occurring at the same time. 2 TYPES OF JOINT PROBABILITY  Mutually Exclusive Event-(without common outcomes)  Non-Mutually Exclusive Event-(with common outcomes) FORMULAS:  Mutually exclusive event P(A and B)=0 P(A or B)=P(A) + P(B)  Non-mutually exclusive event P(A or B)=P(A) + P(B) – P(A∩B) EXAMPLE: Mutually exclusive event A group of teacher is donating blood during blood drive. A student has a 34 135 probability of having a type O blood and a 16 45 probability of having a type A blood. What is the probability that a teacher has type A or O type of blood? Solution: P(AUB)=P(A) + P(B) = 34 135 + 16 45 = 34 135 + 48 135 = 82 135 = 0.6074 or 60.74% 4
7. 7. EXAMPLE: Non-mutually exclusive event What is the probability when you shuffle a deck of cards to get a black card or a 7 card? Solution: P(black card or 7 card)=P(BC) + P(7C) – P(BC Ո 7C) = 26 52 + 4 52 − 2 52 = 30 52 − 2 52 = 28 52 = 7 13 = 0.5384 or 53.84% 5
8. 8. CONDITIONAL PROBABILITY Is the probability of an event (A), given that another event (B) has already occurred. FORMULA: P(A and B)=P(A) × P(B/A) or P(A/B)= P(B and A) P(B) Where: P(A)=prob. Of event A may happen. P(B)=prob. Of event B may happen. P(B/A)=prob. of event B given A. EXAMPLE: dependent event 70% of your friends like Chocolate, and 35% like Chocolate and like Strawberry. What percent of those who like Chocolate also like Strawberry? Solution: P(s/c)= 𝑃(𝐶Ո𝑆) 𝑃(𝐶) = 35% 70% = 1 2 = 0.5 or 50% EXAMPLE: independent event 2 boxes contain of small balls with different color. In the 1st box 2 yellow, 5 red. 2nd box 3 blue, 4 white. What is the probability of getting a red and a white. Formula and solution: P(A and B) = P(A) × P(B) P(R∩W) = P(R) × P(W) = 5 7 × 4 7 = 20 49 =0.4081 or 40.81% 6
9. 9. REPEATED TRIALS PROBABILITY (binomial)  Probability that an event will occur exactly “r” times out of “n” trials.  Also called Bernoulli trial  Binomial trial-is the random experiment with exactly two possible outcomes. (success & failure)  Jacob Bernoulli a Swiss mathematician in 17th century. FORMULA: P=nCr (𝑝) 𝑟 (𝑞) 𝑛−𝑟 Where: p = prob. of success q = prob. of failure n = no. of trials r = successful outcomes EXAMPLE: A die is thrown 6 times. If getting an odd number is a success, what is the probability of 5 successes? Solution: p = 3 6 𝑜𝑟 1 2 q = 3 6 𝑜𝑟 1 2 n = 6 r = 5 P= 6C5( 𝟏 𝟐 ) 𝟓 ( 𝟏 𝟐 ) 𝟔−𝟓 = 𝟑 𝟑𝟐 = 0.0937 or 9.37% 7

Jun. 23, 2021
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Oct. 2, 2018

by Melissa velasco bsed 3

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