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Probability And Statistics: Coin Toss, Odds, And Distributions In Real-World Scenarios

Explore probability and statistics through real-world scenarios in this Assignment Solution.

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    Probability and Statistics: Coin Toss, Odds, and Distributions in Real - World Scenarios 1. (14 pts) There are two coin purses. The first coin purse contains a nickel N and a quarter, Q. The second coin purse contains a dime D and a penny P. From the first purse a coin is randomly chosen, and from the second purse, a coin is randomly chosen, and the outcome is recorded. [For instance, the outcome (N, P) means Nickel from the first purse and Penny from the second purse.] (a) List all of the outcomes in the sample space. There are 4 possible outcomes : ND, NP, QD, QP (b) Let A be the event "the sum of the coin values is an even number of cents." What outcomes belong to event A? (Just list them). We saw there are 4 possible outcomes : ND (15 cent), NP (6 cent), QD (35 cent) and QP (26 cent) : therefore there are two event and two odd amounts, the outcomes that belong to A are {NP, QP} What is the probability of event A? 0.5 There are two event and two odd amounts so the probability of having an even number of cent is : 2/4 = 1/2 = 0.5 (c) Let B be the event "the sum of the coin values is less than 10 cents or greater than 30 cents." What outcomes belong to event B? (Just list them). 6 < 10 and 35 > 30 : then the outcomes that belong to B are {NP, QD} What is the probability of event B? 0.5 2 outcomes out of 4 belong to B : the probability of having the sum of the coin value less than 10 or greater than 30 is : 2/4 = 0.5 (d) Determine the probability P(A  B), where A and B are the events described above. Show work/explanation.

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    P(A  B) = P(A) + P(B) – P(A B ) Where : P(A) = 0.5, P(B) = 0.5, P( A B ) = P(“probability of having an even sum of the coin value less than 10 or greater than 30”) = P({NP}) = 1/4 = 0.25 Therefore : P(A  B) = 0.5 + 0.5 – 0.25 = 0.75 2. (6 pts) The probability that a particular basketball team wins its next game is 4/7. What are the odds for the team winning it next game? What are the odds against the team winning its next game? The odds for the team is determined as follow : 4/(4+3) = 4/7 then the odds for are 4:3 Therefore the odds agai nst are : 3:4

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