Respuesta :
Answer:
33% probability that the company will win at least one of the two contracts
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that a company is awarded the first contract.
B is the probability that a company is awarded the second contract.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a company is awarded the first contract but not the second and [tex]A \cap B[/tex] is the probability that a company is awarded both contract.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
The probability that it will get both contracts is .13.
This means that [tex]A \cap B = 0.13[/tex]
The probability that it will be awarded a second contract is .21
This means that [tex]B = 0.21[/tex]
[tex]B = b + (A \cap B)[/tex]
[tex]0.21 = b + 0.13[/tex]
[tex]b = 0.08[/tex]
The probability that a company will be awarded a certain contract is .25
This means that [tex]A = 0.25[/tex]
[tex]A = a + (A \cap B)[/tex]
[tex]0.25 = a + 0.13[/tex]
[tex]a = 0.12[/tex]
What is the probability that the company will win at least one of the two contracts?
[tex]A \cup B = a + b + A \cap B = 0.12 + 0.08 + 0.13 = 0.33[/tex]
33% probability that the company will win at least one of the two contracts
