MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
During a football tournament, consider the following events for a randomly selected match:
A : The home team scores at least one goal in the first half.
B : The home team wins the match.
(a) Given that P(A)=0.55 and P(B)=0.65, and that P(A′∪B)=0.80, calculate P(A∩B).
(b) Hence find the probability that the home team neither scores in the first half nor wins the match.
(c) Show that the numerical answers obtained are consistent with the axiomatic properties of probability.