Question

22 multiple choice 4 points determine the probability distributions missing value. the probability that a tutor will see 0, 1, 2, 3, or 4 students over the course of one hour is: table of probabilities x 0 1 2 3 4 p(x) 4/27 1/27 5/9? 5/27 1/9 2/27 25/27 -10/27

Explanation:

Step1: Recall probability - sum rule

The sum of all probabilities in a probability distribution is 1. So we need to set up the equation $\sum_{i}P(x_i)=1$.

Step2: Rewrite given probabilities with common denominator

First, rewrite $\frac{5}{9}=\frac{15}{27}$. Let the missing probability be $p$. Then the equation becomes $\frac{4}{27}+\frac{1}{27}+\frac{15}{27}+p+\frac{5}{27}=1$.

Step3: Combine fractions on left - hand side

$\frac{4 + 1+15 + 5}{27}+p=1$, which simplifies to $\frac{25}{27}+p = 1$.

Step4: Solve for $p$

Subtract $\frac{25}{27}$ from both sides of the equation: $p=1-\frac{25}{27}=\frac{27 - 25}{27}=\frac{2}{27}$.

Answer:

$\frac{2}{27}$ (corresponding to option B if the options are labeled as in the multiple - choice setup in the question)