Answer: 0.45
Step-by-step explanation:
Given : 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.
Then,
[tex]P(A\cap B)=P(A)\times P(B)\\\\=0.40\times0.25=0.1[/tex]
Also,
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\=0.40+0.25-0.1\\\\=0.55[/tex]
Now, the probability that the company does not win either project will be :_
[tex]P(A'\cap B')=P(A\cup B)'\\\\=1-P(A\cup B)\\\\=1-0.55=0.45[/tex]
Hence, the probability that the company does not win either project =0.45
