Question

Let A and B be events with =PA0.7, =PB0.2, and =PA and B0.12. (a) Are A and B independent? Explain. (b) Compute PA or B. (c) Are A and B mutually exclusive? Explain. Part 1 of 3 Your Answer is correct (

Answer 1

Answer: a) No, b) 0.78, c) No.

Step-by-step explanation:

Since we have given that

P(A) = 0.7

P(B) = 0.2

P(A∩B) = 0.12

(a) Are A and B independent? Explain.

Since P(A).P(B) = $0.7\times 0.2=0.14$

And P(A∩B) = 0.12

P(A∩B) ≠ P(A).P(B)

So, they are not independent.

(b) Compute P(A or B).

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=0.7+0.2-0.12\\\\P(A\cup B)=0.9-0.12\\\\P(A\cup B)=0.78$

(c) Are A and B mutually exclusive? Explain

Since P(A∩B) ≠ 0

So, they are not mutually exclusive.

Hence, a) No, b) 0.78, c) No.