Probablity problems! Did I do them right?

[noname1234]

user posted message

 

[galactus]

2. Jenny is a general contractor and has submitted two bids for two projects (A and B). The probability of getting project A is 0.65. The probability of getting project B is 0.77. The probability of getting at least one of the two projects is 0.90.
a. What is the probability that she will get both projects?

$\displaystyle P(A and B)=P(A)P(B)$

b. Are the events of getting the two projects mutually exclusive?

Can the two events happen at the same time?. If they're mutually exclusive, then P(A and B)=0

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

Does getting one contract influence the getting of another?.

 

[pka]

Actually in this case we do not have $\displaystyle P(A \cap B) = P(A)P(B).$

What we do have is $\displaystyle P(A \cup B) = 0.9$ and $\displaystyle P(A \cup B) = P(A) + P(B) - P(A \cap B).$

Now solve for $\displaystyle P(A \cap B)$ then you will see that $\displaystyle P(A \cap B) \not= P(A)P(B)$ which will answer part c.