Note that the last property implies f x c for a x b in

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ch side of (A.3) by P (A) gives us the multiplication rule: P (A \ B ) = P (A)P (B |A) (A.4) Intuitively, we think of things occurring in two stages. First we see if A occurs, then we see what the probability B occurs given that A did. In many cases these two stages are visible in the problem. 209 A.1. PROBABILITIES, INDEPENDENCE Example A.4. Suppose we draw two balls without replacement from an urn with 6 blue balls and 4 red balls. What is the probability we will get two blue balls? Let A = blue on the first draw, and B = blue on the second draw. Clearly, P (A) = 6/10. After A occurs, the urn has 5 blue balls and 4 red balls, so P (B |A) = 5/9 and it follows from (A.4) that P (A \ B ) = P (A)P (B |A) = 65 · 10 9 To see that this is the right answer notice that if we draw two balls without replacement and keep track of the order of the draws, then there are 10 · 9 outcomes, while 6 · 5 of these result in two blue balls being drawn. The multiplication rule is useful in solving a variety of problems. To il...
View Full Document

Ask a homework question - tutors are online