Back to Develop a theoretical probability distribution — Problem 1 · Task Set 29

Exercises: Develop a Theoretical Probability Distribution and Find Its Expected Value

Work through each section in order. Show your work where indicated. When you build a probability, separate "the probability of one specific sequence" from "the number of arrangements" that produce that result. Keep fractions over a common denominator so your sum-to-1 check is easy to read.

Grade 11·24 problems·~45 min·Common Core Math - HS Statistics and Probability·group·hss-md-a-3

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Fluency Practice

For the five-question guessing test ( $P(\text{correct}) = \frac{1}{4}$ ), which expression
correctly gives $P(X = 2)$ , the probability of exactly 2 correct?

$\binom{5}{2}\left(\frac{1}{4}\right)^2\left(\frac{3}{4}\right)^3$

$\left(\frac{1}{4}\right)^2\left(\frac{3}{4}\right)^3$

$\frac{1}{6}$ , since $X$ has six possible values $0,1,2,3,4,5$

$\binom{5}{2}\left(\frac{1}{4}\right)^2$