Verizon . 7:17 PM * 80% online.pcc.edu Question 10(1 point) In a particular spor

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Verizon . 7:17 PM * 80% online.pcc.edu Question 10(1 point) In a particular sport, the home team wins the first game of a championship series 57% of the time. when the home team wins the first game of the series they have won the championship 72% of the time. If the home team loses the first game of the series they have won the championship 48% of the time. Assume that all of the said probabilities hold in the long run. Suppose the home team does not win the championship series. What is the probability they won the first game? Write your answer as the exact decimal if the number is less than or equal to the ten- thousandths place, or round to the ten-thousandths place if the decimal is longer

Explanation / Answer

Let 'A' denote the event " They won the first game".

Let 'B' denote the event " Home team does not win the championship".

We need to find Probability(A / B) = P( A / B)

P(A / B ) = P ( A and B ) / P(B)

P(A and B ) = Probability that the home team won the first game and does not win the championship

= 0.57 * ( 1 - 0.72 )

= 0.1596

P(B) = P(Home team does not win the championship)

= Probability that the home team won the first game and does not win the championship + Probability that the home team does not win the first game and does not win the championship

= 0.57 * (1 - 0.72 ) + 0.43 * ( 1 - 0.48 )

= 0.2236

P(A / B ) = P ( A and B ) / P(B) = 0.1596 / 0.2236 = 0.7138

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