Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the probabilities P(E, ) = 0.1, P(E2) = 0.2, P(E3) = 0.2, P(E4) = 0.2, and P(E5) = 0.3. Complete parts a through d. A a. Calculate P(A), P(B), and P(AnB). P(A) = (Type an integer or a decimal.) P(B) = (Type an integer or a decimal.) P(AnB) = (Type an integer or a decimal.) b. Suppose event A has occurred, so that the reduced sample space consists of the three sample points in A-namely, E1, E2, and Eg. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P(E |A)]. Find the ratio of the conditional probabilities to verify that they are in the same proportion to one another as the original sample point probabilities. Calculate P(E, |A), P(E2|A ), and P(E3 / A) . P(E, IA) = ]. P(E2/A) = ]. P(E3IA) = ] (Type integers or decimals.) Write the ratio of P(E, [A) to P(E2|A) to P(E3|A) using the smallest integers possible. to to ](List the terms in the same order as they appear in the original list.) c. Calculate the conditional probability P(BIA) in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection AnB, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability, as shown below. P(AnB) P(B|A) = - P (A ) What is P(BIA)? P(B|A) = (Type an integer or a decimal.)