Answer to Question #305535 in Statistics and Probability for john

Question

Tom has a 0.5 chance of winning the Booker Prize, whereas John has a 0.4 chance of winning the Booker Prize. Only one Booker prize is up for grabs. How likely is it that at least one of them will win the prize?

Answer 1

Let A - "at least one of them will win the prize"

$H_1-$ "Tom won"

$H_2-$ "John won"

Then, $P(A)=P(H_1)*P(\neg H_2)+P(\neg H_1)*P(H_2)+P(H_1\cap H_2)=0.5*0.6+0.5*0.4+0=0.5$