Question

probability distributions
probability distribution table
sum
frequency
probability
2
1
\\(\frac{1}{9}\\)
3
2
\\(\frac{2}{9}\\)
4
3
\\(\frac{3}{9}\\)
5
2
\\(\frac{2}{9}\\)
a.
probability
\\(\frac{1}{9}\\) \\(\frac{2}{9}\\) \\(\frac{3}{9}\\) \\(\frac{2}{9}\\) \\(\frac{5}{9}\\) \\(\frac{4}{9}\\)
sum
2 3 4 5 6
b.
probability
\\(\frac{1}{9}\\) \\(\frac{2}{9}\\) \\(\frac{3}{9}\\) \\(\frac{2}{9}\\) \\(\frac{5}{9}\\) \\(\frac{4}{9}\\)
sum
2 3 4 5 6
c.
probability
... \\(\frac{3}{9}\\) \\(\frac{4}{9}\\) \\(\frac{5}{9}\\)
...
d.
probability
... \\(\frac{3}{9}\\) \\(\frac{4}{9}\\) \\(\frac{5}{9}\\)
...
check answer

Explanation:

Step1: Identify given probabilities

From the table:
$P(\text{Sum}=2)=\frac{1}{9}$, $P(\text{Sum}=3)=\frac{2}{9}$, $P(\text{Sum}=4)=\frac{3}{9}$, $P(\text{Sum}=5)=\frac{2}{9}$

Step2: Match to histogram

Find the histogram where each sum's bar height matches its probability. Option A has bars with the exact heights from the probability distribution table.

Answer:

A. (The histogram where the bars for sums 2,3,4,5 have heights $\frac{1}{9}$, $\frac{2}{9}$, $\frac{3}{9}$, $\frac{2}{9}$ respectively)