Probability word problem

Question

Two tennis players are said to have a probability of 2/5 and 3/4 respectively of winning a tournament. Find the probability that a) 1 of them will win

b) neither of them will win

Answer 1

part a) I take it that the question is asking at least one of them will win;

P(A)=2/5=40%

P(B)=3/4=75%

Then P(A∩B)=2/5*3/4=6/20=30%

P(A∪B)=p(A)+P(B)-P(A∩B)=2/5+3/4-6/20=17/20=85%

 

part b) Neither of them win is that none of them win, that is P(∼A∩∼B) which is equivalent to 1-P(A∪B)=1-17/20=3/20

 

best wishes,

Bader A.