Consider the experiment defined by the accompanying Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P1E12 = .1, P1E22 = .1, P1E32 = .2, P1E42 = .5, P1E52 = .1.

a. Calculate P(A), P(B), and P1A ¨ B2.

b. Suppose we know that event A has occurred, so the reduced sample space consists of the three sample points in A: E1, E2, and E3. Use the formula for conditional probability to determine the probabilities of these three sample points given that A has occurred. Verify that the conditional probabilities are in the same ratio to one another as the original sample point probabilities and that they sum to 1.

c. Calculate the conditional probability P1BA2 in two ways: First, sum P1E2 A2 and P1E3 A2, since these sample points represent the event that B occurs given that A has occurred. Second, use the formula for conditional probability:

Verify that the two methods yield the same result.

Transcribed Image Text:

E E2 E30 A E40 Es B S