1. 1. Two identical components operating in parallel share a common load. If one component fails, the probability that the other component fails increases as a result of the increased load placed on it. Let A and B be the event that component 1 fails and the event that component 2 fails, respectively. If P(A) = P(B) = 0.05 and P(A|B) = P(B|A) = 0.10.

Find the probability of event where both components fail.

1. 2. In the game of craps, a player rolls two balanced dice. Thirty-six equally likely outcomes are possible. Let

A = event the sum of the dice is 6,

B = event the sum of the dice is 7,

C = event the sum of the dice is 4,

D = event the sum of the dice is 2,

E = event the sum of the dice is 10,

F = event the sum of the dice is 8,

G = event doubles are rolled.

1. Compute the probability of each of the seven events. P(A)P(B)P(C) P(D) P(E)P(F)P(G)

1. The player wins on the first roll if the sum of the dice is 6 or 7. Find the probability of that event. The player loses on the first roll if the sum of the dice is 4, 2, or 10. Determine the probability of that event.

1. Computetheprobabilitythateitherthesumofthediceis8ordoublesarerolled.
3. 3. One card is selected at random from an ordinary deck of 52 playing cards. Let

A = event a face card is selected,

B = event a king is selected, and

C = event a heart is selected.

Find the following probabilities and express your results in words.

1. P (B)
2. P (B|A)

1. P (B|C)
2. P (B|(not A))

1. P (A)
2. P (A|B)

1. P (A|C)