slides_1_probability

# 55 sometimes we are given conditional probabilities

This preview shows pages 55–64. Sign up to view the full content.

55

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Sometimes we are given conditional probabilities and we need to compute the probability that several events occur simultaneously. Using the definition of conditional probability we can always write P A B P A | B P B so that, given P B and the conditional probability P A | B , we can find P A B . 56
We can extend this to many events by applying this representation repeatedly: P A k A k 1 A 1 P A k | A k 1 A 1 P A k 1 A 1 P A k | A k 1 A 1 P A k 1 | A k 2 A 1 P A k 2 A 1 and so on, to get P A k A k 1 A 1 P A k | A k 1 A 1 P A k 1 | A k 2 A 1 P A 2 | A 1 P A 1 57

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
By simply reversing the order of events we can also write the relationship – which is useful for sequential experiments – as P A 1 A 2 A k P A 1 P A 2 | A 1  P A k 1 | A k 2 A 1 P A k | A k 1 A 1 58