1.You are given thatP[A] = 0.5 and P[A B] = 0.7

Actuary 1 assumes that A and B are independent and calculates P[B] based on that assumption.

Actuary 2 assumes that A and B mutually exclusive and calculates P[B] based on that assumption.

Find the absolute difference between the two calculations.

2.Two bowls each contain 5 black and 5 white balls. A ball is chosen at random from bowl 1 and put into bowl 2. A ball is then chosen at random from bowl 2 and put into bowl 1. Find the probability that bowl 1 still has 5 black and 5 white balls.

3.A system has two components placed in series so that the system fails if either of the two components fails. The second component is twice as likely to fail as the first. If the two components operate independently, and if the probability that the entire system fails is .28, find the probability that the first component fails.

4.In the game show "Let's Make a Deal", a contestant is presented with 3 doors. There is a prize behind one of the doors, and the host of the show knows which one. When the contestant makes a choice of door, at least one of the other doors will not have a prize, and the host will open a door (one not chosen by the contestant) with no prize. The contestant is given the option to change his choice after the host shows the door without a prize. If the contestant switches doors, what is the probability that he gets the door with the prize?

5.Let A, B, and C be mutually independent events such that P[A] = 0.5,P[B] = 0.6, and P[C] = 0.1. Calculate P[A B C]

6.An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44 Calculate the number of blue balls in the second urn.

7.LetA,B,CandDbeeventssuchthatB=A,(CD)=0, andP[A]=14,P[B]=

31311

4 , P [C|A] = 2 , P [C|B] = 4 , P [D|A] = 4 , P [D|B] = 8 . Calculate P [C D]