Probability Example: A vs B | Competing Software Companies

[r0bHadz]

Homework Statement

I was reading this example in a book...

"
Two competing software companies are after an important contract. Company
A is twice as likely to win this competition as company B. Hence, the probability to
win the contract equals 2/3 for A and 1/3 for B."

Homework Equations

The Attempt at a Solution

What is the significance of the word "twice as likely?" It seems to me like if company 1 had a probability of .5, then there is no way company 2 had a probability of 1

And where did they get the 3 in the denominator of the fraction? How can we know that its not 2/7 and 4/7 for the two companies?

 

[mfb]

It seems to me like if company 1 had a probability of .5, then there is no way company 2 had a probability of 1

Yes, the events "company 1 is twice as likely to win" and "company 1 has 0.5 probability" exclude each other.

And where did they get the 3 in the denominator of the fraction? How can we know that its not 2/7 and 4/7 for the two companies?

The problem makes the assumption that exactly one of them will win the contract. P(A)+P(B)=1. Together with P(B)=2P(A) you can calculate the probabilities.