Probability and Statistics: Coin Toss, Odds, and Distributions in Real-World Scenarios1. (14 pts) There are two coin purses. The first coin purse contains a nickel N and aquarter, 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 israndomly chosen, and the outcome is recorded.[For instance, the outcome (N, P) meansNickel from the first purse and Penny from the second purse.](a) List all ofthe outcomes in the sample space.Thereare 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 4possible outcomes : ND (15 cent), NP (6 cent), QD (35 cent) and QP (26cent) : 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?0.5There are two event and two odd amounts so the probability of having an even number ofcent 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 30cents."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?0.52 outcomes out of 4 belong to B : the probability of havingthe sum of the coinvalue lessthan 10 or greater than 30 is : 2/4 = 0.5(d) Determine the probability P(AB), where A and B are the events described above. Showwork/explanation.Preview Mode
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