Answer to Question #340135 in Statistics and Probability for Maneo

Question

A contractor has submitted bids for two state construction projects. The probability that he will be awarded any contract is 0.3 and it is the same for each of the two contracts.

1) - What is the probability that he will be awarded both contracts?

2) - What is the probability that he will be awarded neither contract?

Answer 1

We have a Bernoulli trial - exactly two possible outcomes, "success" (the contractor is awarded the contract) and "failure" (the contractor isn't awarded the contract) and the probability of success is the same every time the experiment is conducted (the contractor submits a bid for a contract), $p=0.3, q=1-0.3=0.7, n=2.$

The probability that I guess on k correct answers

$P(X=k)=\begin{pmatrix}n\\k\end{pmatrix}\cdot p^k\cdot q^{n-k}=\\ =\begin{pmatrix}2\\k\end{pmatrix}\cdot 0.3^k\cdot 0.7^{2-k}=\\ =\cfrac{2!}{k!\cdot(2-k)!}\cdot 0.3^k\cdot 0.7^{2-k}.$

1) The probability that he will be awarded both contracts

$P(X=2)=\cfrac{2!}{2!\cdot0!}\cdot 0.3^{2}\cdot 0.7^{0}=0.09.$

2) The probability that he will be awarded neither contract

$P(X=0)=\cfrac{2!}{0!\cdot2!}\cdot 0.3^{0}\cdot 0.7^{2}=0.49.$