Question

A company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25. Winning project A and winning project B are independent events. What is the probability that the company wins project A or project B

Answer 1

Answer:

Probability that the company wins project A or project B is 0.50.

Step-by-step explanation:

We are given that a company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25.

Also, Winning project A and winning project B are independent events.

Let the Probability of winning project A = P(A) = 0.40

            Probability of winning project B = P(B) = 0.25

Now, as we know that ;

Probability that the company wins project A or project B = $P(A \bigcup B)$

              $P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B)$

So, we have to find the value of Probability of winning project A and B, i.e;

$P(A \bigcap B)$

Since, we are given that Winning project A and winning project B are independent events which means when this condition is given then;

                    $P(A \bigcap B) = P(A) \times P(B)$

                                    = 0.40 $\times$ 0.25 = 0.10

Now, Probability that the company wins project A or project B is given by;

                 $P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B)$  

                                  = 0.40 + 0.25 - 0.10

                                  = 0.65 - 0.10 = 0.55

Hence, probability that the company wins project A or project B is 0.50.