Back to Develop a theoretical probability distribution — Problem 2 · 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

Work through problems with immediate feedback

Recall / Warm-Up

A student guesses on every question of a five-question test where each question has four
equally likely choices. Let $X$ be the number of questions answered correctly. Which statement
correctly describes the model?

$P(\text{correct}) = \frac{1}{4}$ , $P(\text{wrong}) = \frac{3}{4}$ , and the questions are independent.

$P(\text{correct}) = \frac{1}{2}$ because each answer is either right or wrong.

$P(\text{correct}) = \frac{1}{4}$ , but the questions are dependent on one another.

$P(\text{correct}) = \frac{3}{4}$ because there are three wrong choices.