Suppose the probability that a construction company will be awarded certain contract is .25, the probability that it will be awarded a second contract is .21, and the probability that it will get both contracts is .13. What is the probability that the company will win at least on of the two contracts?

there are 3 scenarios

1. win the first, lose the second ---> .25(.79) = ...

2. lose the first, win the second ---> .75(.21) = ...

3. win the first, win the second ---> .25(.21) = ....

add them up

What about the number given, .13 for get both contracts? Wouldn't that contradict the third scenerio?

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

add the probabilities of getting each contract then subtract the probability of getting both contracts

To find the probability that the company will win at least one of the two contracts, we can use the principle of inclusion-exclusion.

First, let's calculate the probability that the company will win the first contract only. This can be found by subtracting the probability of winning both contracts from the probability of winning the first contract:

P(first contract only) = P(first contract) - P(both contracts)
P(first contract only) = 0.25 - 0.13
P(first contract only) = 0.12

Similarly, we can calculate the probability of winning the second contract only:

P(second contract only) = P(second contract) - P(both contracts)
P(second contract only) = 0.21 - 0.13
P(second contract only) = 0.08

Next, let's find the probability of winning neither contracts. This can be obtained by subtracting the sum of the probabilities of winning the first contract only and winning the second contract only from 1 (since the sum of all possible outcomes must equal 1):

P(neither contract) = 1 - (P(first contract only) + P(second contract only))
P(neither contract) = 1 - (0.12 + 0.08)
P(neither contract) = 1 - 0.20
P(neither contract) = 0.80

Finally, to find the probability that the company will win at least one of the two contracts, we subtract the probability of winning neither contracts from 1:

P(at least one contract) = 1 - P(neither contract)
P(at least one contract) = 1 - 0.80
P(at least one contract) = 0.20

Therefore, the probability that the company will win at least one of the two contracts is 0.20, or 20%.