Question

Please provide all answers according to question numbers with steps thank you

B Bc (4) For two events A and B, suppose: A 0.3 0.4 Then P(AUB) is equal to? Ac 0.1 0.2 (5) Suppose P(A) 0.4, P(B) 0.3, and P(An B) 0.12. Which one of the following statements correctly defines the relationship between events A and B? (a) Events A and B are independent, but not mutually exclusive (b) Events A and B are mutually exclusive, but not independent cEvents A and B are neither lly exclusive nor independent (d) Events A and B are both mutually exclusive and independent (6) Suppose P(A) 0.80, P(B)0.60 and P(AUB)-0.90. Then what is the value of P(A|B)? (7) From experience, a shipping company knows that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment but guarantees to refund the charge if delivery is not made within 24 hours. I the company fails to deliver only 2% of its packages within the 24-hour period, what is the expected gain per package?

Answer 1

4)P(A u B)=P(A)+P(B)-P(A n B)=(0.3+0.4)+(0.3+0.1)-0.3=0.8

5)AS P(A n B)=P(A)*P(B)

option A is correct

6)

P(A n B)=P(A)+P(B)-P(A n B)=0.8+0.6-0.9=0.5

hence P(A|B)=P(A n B)/P(B)=0.5/0.6=5/6

7)

expected gain per package =0.98*(15.50-14.80)-0.02*14.80=$0.39