what is the probability that the yankees will win when they score 5 or more runs

Question

this season, the probability that the yankees will win a game is 0.57 and the probability that the yankees will score 5 or more runs in a game is 0.6. the probability that the yankees lose and score fewer than 5 runs is 0.31

Answer 1

Hi Haylee C.,

I guess you're being asked to apply Bayes's (aka Bayes') Theorem. You should definitely know how to use that, it will save you time!

So, it is P(A|B) = P(B|A)*P(A)/P(B) where |means "given that"

So A = they win

and B = they score 5 or more runs

So P(A) is given at 0.57 and P(B) is given at 0.6 . But what is P(B|A)? Not so easy to see how to go about determining, is it?

So draw yourself a rectangular Venn diagram instead, sectioned off into 4 rectangular boxes, 2 across by 2 down. label the top edge: W, and the bottom edge: L for won and lost respectively (applies to top and bottom sections of box respectively)

label the left edge <5, and the right edge >=5, for runs Yankees score. (again, for left sections and right sections respectively)

Start filling in: 0.57 is top two total. 0.31 is bottom left box only, 0.6 is right two boxes total.

You can see now, easily, that the 0.6 must be distributed somehow between right top and right bottom.

Assign the top right box the value "x". Then the bottom right box has value 0.6 - x , and you can set up an equation for things: (0.6-x)+0.31 = [total bottom] = 0.43 (since top was 0.57). Solve: x = 0.48 , and the ducks rapidly fall in a row as bottom right = 0.12, top right = 0.48, top left = 0.09.

Trivially, the query resolves into top right/right total = 0.48/0.6 = 0.8

-- Cheers, -- Mr. d.