Back to Develop a theoretical probability distribution — Problem 4 · 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

Fluency Practice

The full developed distribution for the five-question guessing test is shown below.

$k$	0	1	2	3	4	5
$P(X=k)$	$\frac{243}{1024}$	$\frac{405}{1024}$	$\frac{270}{1024}$	$\frac{90}{1024}$	$\frac{15}{1024}$	$\frac{1}{1024}$

Add the six numerators to verify the distribution is valid. What is the sum of the numerators?