Lesson A company bids on two separate contracts

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A company bids on two separate contracts

Problem 1

An aerospace company has submitted bids on two separate federal government defense contracts.
The company president believes that there is a 57% probability of winning the first contract.
If they win the first contract, the probability of winning the second is 67%.
However, if they lose the first contract, the president thinks that the probability
of winning the second contract decreases to 44%.
What is the probability that they lose both contracts?

Solution

Step by step.

P(win 1st contract)  = P(1) = 0.57  (given).

P(lose 1st contract) = 1 - 0.57 = 0.43  (the complement).


P(win  2nd contract) = P(2) = 0.57*0.67 + (1-0.57)*0.44 = 0.5711.


P(win both 1st and 2nd contracts) = 0.57*0.67 = 0.3819.


P(win at least one of the two contracts) = P(1) + P(2) - P(both) = 0.57 + 0.5711 - 0.3819 = 0.7592.

P(lose both) = 1 - P(win at least one of the two contracts) = 1 - 0.7592 = 0.2408.    ANSWER

Problem 2

A contract company has bid on two contracts. The probability of winning contract A is 0.71.
If the company wins contracts A, the probability of winning contract B is 0.62.
If the company loses contract A, the probability of winning contract B decreases to 0.33.
What is the probability of not winning any contract?

Solution

Step by step.

(a)  P(A win) = 0.71   (given).


(b)  P(both A and B win) = 0.71*0.62 = 0.4402.


(c)  P(B win) = 0.71*0.62 + (1-0.71)*0.33 = 0.5359.


(d)  P(A or B win) = P(A win) + P(B win) - P(both A and B win) = 0.71 + 0.5359 - 0.4402 = 0.8057.


(e)  P(not winning any contract) = complement of (d) to 1 = 1 - 0.8057 = 0.1943.    ANSWER

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