Answer to Question #166677 in Statistics and Probability for Bikram Chaudhary

Question

A, B and C are bidding for a contract. It is believed that A has exactly half the chance that B has, B in turn 4/5th as likely as C to win the contract. What is the probability for each to win the contract?

Answer 1

Let probability of C winning be x

Therefore probability of B winning is $\dfrac{4x}{5}$

and probability of A winning is $\dfrac{4x}{10}$

Sum of the probabilities should be equal to 1

So, $\dfrac{4x}{5} +\dfrac{4x}{10}+x=1$

$\Rightarrow x=\dfrac{5}{11}$

Therefore,

A has a probability of $\dfrac{2}{11}$ for winning the contract.

B has a probability of $\dfrac{4}{11}$ for winning the contract.

C has a probability of $\dfrac{5}{11}$ for winning the contract.