Yvonne and Novac play two games of tennis every Saturday. Yvonne has a 65%
chance of winning the first game and, if she wins it, her chances of winning
the second game increase to 70%. However, if she loses the first game, then her
chances of winning the second game decrease to 55%. Find the probability that
Yvonne:
a loses the second game
b wins the first game, given that she loses the second game
Answers
Answer:
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Answer:
a.
chances of losing the second game ,
0.65 x 0.3 + 0.35 x 0.45
= 0.3525 (1)
b. chances of winning the first game given that she loses the 2 nd game,
0.5532
explanation for a
probability of Yvonne winning the 1 st game x probability of him LOSING the second + probability of him losing the 1 st game and LOSING the 2 nd game
explanation for b
the probability of winning/losing the 1 st game given that he has lost the 2 nd game,
total sample size = 0.3525 as it is given that he has lost the 2 nd game ,
the probability that he has wina the 1st and loses2 nd game is
(0.65 x 0.3) ÷ 0.3525 (refer 1)
= 0.5532
or
according to Bayes formula,
P(A/B) = { P ( B/A ) x P (A) } ÷ { P (B/A) x P (A) + P (B/A') x P (A')}
THUS ,
P(A/B) = (0.65 x 0.3) ÷ 0.3523 ( refer 1)
= 0.5532