Question

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.

Answer #1

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**

?In an article titled “Unilateral Nostril Breathing Influences
Lateralized Cognitive Performance” that appeared in Brain and
Cognition (1989), researchers Block et al. published results from
an experiment involving assessments of spatial and verbal cognition
when breathing through only the right versus left nostril. The
subjects were 30 male and 30 female right-handed introductory
psychology students who volunteered to participate in exchange for
course credit. Initial testing on spatial and verbal tests revealed
the following summary statistics. Note that the scores...

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