Question

Anna challenges Sarah to a game where Sarah flips a fair coin and then randomly chooses a card from a small deck of cards that includes only 111 jack, 111 queen, 111 king, and 111 ace.The only way Sarah can win is by flipping heads and then choosing either the jack or the queen.If XXX is a random variable that represents Sarah's outcome, drag the bars to graph the probability distribution for all possible values of XXX.

Answer 1

The probability distribution for all possible values of X are given in the discrete probability table ;

• X : ____ winning ____ not winning

• P(X) : ____ 0.25 ________ 0.75

Fair coin = {H, T}

card = {J, Q, K, A}

Sample space :

• __ H ___ T
• J | HJ __ TJ
• Q| HQ __TQ
• K| HK __ TK
• A| HA __ TA

• Total possible outcomes = sample space = 8

• Winning selection = {HJ, HQ}

Probability of winning ; P(Winning) = 2/8 = 1/4 = 0.25

Probability of not winning ;

1 - P(wininng) = 1 - 1/4 = 3/4 = 0.75

X : ____ winning ____ not winning

P(X) : ____ 0.25 ________ 0.75

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