The prior probabilities for events Aj and Ag are P(A1) = 0.50 and P(A2) = 0.50. It is also known that P(A n A2) = 0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.70. a. Are events Aj and Az mutually exclusive? Yes Explain. i) P(A1 N A2) = o Ci) P(A1) + P(A2) = 1 (iii) P(A2) = P (A2 | A1) (iv) P(A2) = P(A2 | A1) choice (i) b. Compute P(A N B) (to 2 decimals). 0.165 Compute P(A3 N B) (to 2 decimals). 0.4819 =. Compute P(B) (to 2 decimals). 0.415 1. Apply Bayes' theorem to compute P(A1|B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).

Q: Suppose that A and B are independent events such that P(A) = 0.3 and P(B) = 0.2. Find P(A&B).

A: The Special Multiplication Rule (for two independent event)

Q: 10. P(A) = 0.5 and P(A + B) = 0.7, find P(B) if – %3D (i) A and B are independent events; (đi) A and…

A:

Q: 2.The probability that Samantha will be accepted by the college of her choice and obtain a…

A: It is an important part of statistics . It is widely used .

Q: Suppose that E and F are two events and that P(E) = 0.5 and P(F|E) = 0.2. What is P(E and F)? P(E…

A: GivenP(E)=0.5P(F|E)=0.2

Q: For two events, A and B, P(A) = 0.5, P(B) = 0.5, and P(A/B) = 0.4. a. Find P(ANB). b. Find P(BIA).…

A:

Q: If B CA and A and B are two events such that P (A) = 3 P (B) and A UB = S find P (B) ?

A: Answer: For the given data,

Q: Suppose that E and F are two events and that N(E and F)=420 and N(E)=740. What is P(F|E)?

A:

Q: 27. If P (A) = 0.5, P (B) = 0.3, P (AB) = 0.2, obtain the probability that (i) A occurs but not B…

A:

Q: Suppose that E and F are two events and that P(E) = 0.5 and P(FIE) = 0.3. What is F P(E and F)=…

A: We have given that,  If E and F are two events with,  P(E) = 0.5, P(F|E) = 0.3 Then,  P( E and F ) =…

Q: Let A and B be events with P(A) = 0.5, P(B) = 0.4. Assume that A and B are independent. Find P(A and…

A: Here the events are indepenedent P(A) = 0.5 P(B) = 0.4

Q: Suppose A and B are mutually exclusive events. P(A)= 0.33, P(B)= 0.30 Calculate P(A or B)?

A: Answer: Given that, A and B are mutually exclusive events P(A) = 0.33 P(B) = 0.30

Q: Suppose that A and B are two events for which P(A)=0.31, P(B)=0.68, and P(AandB)=0.31 Find P(A|B)

A: According to the given information, we have There are two events A and B i.e. P(A) = 0.31 P(B) =…

Q: Suppose P and Q are two independent events with P(P) = 0.23, P(P and Q)= 0.18 Calculate P

A: P(P) = 0.23, P(P and Q)= 0.18 P and Q are independent events

Q: Let A and B be two events, and P(A) = 1/2, P(B) = 1/5 and P(B|A) = 1/3. Find the value of P(A|B).

A: