The prior probabilities for events A1 and A2 are P(A1) = .40 and P(A2) = .60. It is also known that P(A1 ∩ A2) = 0. Suppose P(B ∣ A1) = .20 and P(B ∣ A2) = .05.a. Are A1 and A2 mutually exclusive? Explain.b. Compute P(A1 ∩ B) and P(A2 ∩ B).c. Compute P(B).d. Apply Bayes’ theorem to compute P(A1∣ B) and P(A2 ∣ B)

Suppose we know that the probabilities P(A) = .5, P(B|A) = .3 and P(A or B) =.3. What is the value for P(A and B)? What is the value for P(B)?

Answer A,B,C

and V are mutually exclusive events. P(U) = 0.29; P(V) = 0.52. Find:  a.  P(U and V) =  b.   P(U|V) =  c.  P(U or V) =

Let A and B be two events such that P(ANB)=0.2, P(A NB)=D0.3 , and P(ANB)3D0.7. The value of P(B | A) is Select one: a. 1 b. 3 < O O

U and V are mutually exclusive events. P(U) = 0.21; P(V) = 0.43. Find:  a.  P(U and V) =  b.   P(U|V) =  c.  P(U or V) =

By rewriting the formula for the multiplication rule, you can write a formula for finding P(A and B) conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B A) = Use the information below to find the probability that a flight P(A) departed on time given that it arrives on time. The probability that an airplane flight departs on time is 0.89. The probability that a flight arrives on time is 0.87. The probability that a flight departs and arrives on time is 0.83. The probability that a flight departed on time given that it arrives on time is (Round to the nearest thousandth as needed.)

U and V are mutually exclusive events. P(U) = 0.32; P(V) = 0.48. Find: a. P(U and V) = b. P(U|V) = c. P(U or V) =