If P()=0.3P(A)=0.3, P()=0.4P(B)=0.4, and P(∪)=0.7P(A∪B)=0.7, then P(∩)=P(A∩B)= . (a) Are events A and B independent? (enter YES or NO) (b) Are A and B mutually exclusive? (enter YES or NO)

(a) No

(b) Yes

Step-by-step explanation:

It is provided that:

P (A) = 0.30

P (B) = 0.40

P (A ∪ B) = 0.70

Compute the value of P (A ∩ B) as follows:

P (A ∩ B) = P (A) + P (B) - P (A ∪ B)

(a)

If events X and Y are independent then,.

Check whether A and B are independent or not as follows:

Thus, the events A and B are not independent.

(b)

If events X and Y are mutually exclusive then,.

Check whether A and B are mutually exclusive or not as follows:

Thus, the events A and B are mutually exclusive.

$30.32

step-by-step explanation:

65.00*.12=2.80

65.00-2.80=57.20

57.20*1.06=60.632

60.632/2=30.316

1. perpendicular

2. parallel

3. perpendicular