Find probablilty give Probablitlies

Question

This season, the probability that the Yankees will win a game is 0.61 and the probability that the Yankees will score 5 or more runs in a game is 0.49. The probability that the Yankees lose and score fewer than 5 runs is 0.3. What is the probability that the Yankees will lose when they score 5 or more runs? Round your answer to the nearest thousandth.

Answer 1

p(w) =.61

p(5) =.49

p(L&not5)=.3

p(L&5) =.09= 9%

P(L)=.39

P(not5) =.51

4 mutually exclusive disjoint outcumes

w&5, L&not5, L&5, w&not5

assuning no ties

p(w&5)+p(L&not5)+p(L&5)+p(w&not5)=1

draw a venn diagram

.21 +.30+.09+.4=1

p(w&not5)=.4

but if ties, then you can get tied up in knots figuring this out

but you know 2 things

P(w) = .61

P(L&not5)=.30

Maybe they tie .09 and never Lose with 5 or more runs

if by chance you interpret the problem as a conditional probability problem

then again use the Venn diagram and get P(L/5) = .3/.51 =about .58824 = 58.824%

assuming no ties

but if ties then ...

You can solve the problem with Bayes Theorem, but it's easier to see visually what's going on with Venn diagrams.It's easier to make a mistake with Bayes. either way you get the same answer, about 1/10 or 3/5 depending on what you want, the intersection or conditional

Answer 2

Answer 3

The probability that the Yankees will lose is 1 - 0.61 = 0.39; if the probability that the Yankees will lose and score fewer than 5 run is 0.3, then the probability that the Yankees will lose and score 5 or more runs is 0.39 - 0.3 = 0.09