Question

# Ethan, Matt and Adam are three friends who participate in a monthly math competition. Each month,...

Ethan, Matt and Adam are three friends who participate in a monthly math competition. Each month, the probability that Ethan will score higher than Matt is 50%; the probability that Ethan will score higher than Adam is 90%; the probability that Ethan will score higher than neither Mat nor Adam is 5%. 1. Find the probability that Ethan scores higher than at least one of his two friends. 2. Find the probability that Ethan scores higher than Adam but not Matt. 3. Find the probability that Ethan scores higher than both Matt and Adam.

let E represent Ethan,M represent Matt,A represent Adam

probability that Ethan will score higher than Matt ,P(E>M)=0.5

P(E<M)=0.5

the probability that Ethan will score higher than Adam ,P(E>A)=0.9

,P(E<A)=0.1

the probability that Ethan will score higher than neither Mat nor Adam=0.05

A)the probability that Ethan scores higher than at least one of his two friends=P(E>M)*P(E<A)+P(E>A)*P(E<M)+P(E>M)*P(E>A)

=0.5*0.1 + 0.9*0.5 + 0.5*0.9

=0.05 + 0.45 + 0.45 = 0.95

B)the probability that Ethan scores higher than Adam but not Matt=P(E>A)*P(E<M)

=0.9*0.5=0.45

C)the probability that Ethan scores higher than both Matt and Adam=P(E>M)P(E>A)=0.9*0.5=0.45

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