A college professor classifies his students according to their grade point avera

Question

A college professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors). One student is selected at random. The table below provides joint probabilities.

Calculate the probability that the randomly selected student is in the Upper Class. Enter your answer in decimal form and round to your answer to three decimal places.

GPA 2.5 or less Above 2.5 Under Class 0.18 0.15 Upper Class 0.26 ?

Explanation / Answer

we have given joint probability table and we know that the sum of marginal probability is equal to 1.

let assume the probability of randomly selected student is in Upper class is X.

and 0.44 + 0.15 + X = 1

so X = 1 - 0.59

X = 0.41

thus the required probability is 0.41

under class 0.18 0.15 upper class 0.26 X marginal 0.44 0.15+X

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