Question

1. Tammy is a general contractor and has submitted two bids for two projects (A and B). The probability of getting project A is 0.55. The probability of getting project B is 0.78. The probability of getting at least one of the projects is 0.91.

a. What is the probability that she will get both projects?

b. Are the events of getting the two projects mutually exclusive? Explain, using probabilities.

c. Are the two events independent? Explain, using probabilities.

Answer 1

a)

Using addition rule of probabilities

P(A OR B) = P(A) + P(B) - P(A and B)

0.91 = 0.55 + 0.78 - P( A and B)

So,,

P(A and B) = 0.55 + 0.78 - 0.91

= 0.42

b)

Two events are mutually exclusive if P( A and B) = 0

Since P(A and B) = 0.42 0, Events A and B are not mutually exclusive.

c)

Two events A and B are independent if P(A and B) = P(A ) * P(B)

Now ,

P(A ) * P(B) = 0.55 * 0.78 = 0.429

Since

P(A and B) P(A) * P(B) , Events A and B are not independent.