Back to Using Probability to Make Decisions — Problem 3 · Task Set 38

HSS.MD Tutor Intake - Random Variables, Expected Value, and Decisions

This short diagnostic helps your tutor see where to start in the Using-Probability-to-Make-Decisions unit. Every topic here is advanced (STEM-track) material, so a few items assume you have opted into it. Answer each question on your own, without help. If you are unsure, give your best attempt - a wrong answer still tells your tutor what to review.

Grade 11·12 problems·~16 min·Common Core Math - HS Statistics and Probability·domain·md

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Procedures

On a 5-question multiple-choice quiz with 4 choices each, a student
guesses every answer, so each question is correct with probability
$\frac{1}{4}$ . Which expression gives $P(X = 2)$ , the probability of
exactly 2 correct?

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

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

$\frac{1}{4} + \frac{1}{4}$

$\frac{1}{6}$ , since $X$ can be 0, 1, 2, 3, 4, or 5.