MBA Math Sample Exercise

Statistics: Probability

Moving well beyond generic GMAT aptitude questions, the MBA Math sample exercises allow prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.

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Exercise

Let X be a discrete random variable. If Pr(X<5) = 2/9, and Pr(X<=5) = 5/18, then what is Pr(X=5)?

Solution

Solution Commentary

(2:23)

Manual Solution

The key realization to solving this problem is to recognize that the range specified by the second subset (X<= 5) consists of the range specified by the first subset(X<5) and the subset of interest (X=5).
Similarly, the probability of the second subset is equal to the sum of the probabilities of the first subset and the subset of interest. In other words, the probability of the subset of interest is the difference between the probabilities of the two subsets. Thus,

Pr(X= 5)= Pr(X<= 5) -Pr(X<5)
Pr(X= 5)= 5/18 - 2/9
Pr(X=5) = 5/18 - 4/18
Pr(X=5) = 1/18

Peter Regan teaches decision science courses at Dartmouth’s Tuck School and Duke’s Fuqua School. He also teaches pre-term quantitative skills courses at Tuck and Cornell’s Johnson School. He created the MBA Math self-paced, online pre-MBA quantitative skills course covering finance, accounting, economics, statistics, and spreadsheets.