Question

1. let r = the number of times a family dines out for dinner in a randomly selected week. the possible values of r with corresponding probabilities are shown in the table.

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$$\begin{array}{c|c|c|c|c|c|c}r & 0 & 1 & 2 & 3 & 4 & 5 \\\\ \\hline p(r) & 0.15 & 0.20 & 0.10 & 0.10 & 0.15 & 0.20\\end{array}$$

is this a valid probability model? explain your answer.

Explanation:

Step1: Check individual probabilities

All given $P(R)$ values ($0.15, 0.20, 0.10, 0.10, 0.15, 0.20$) are between $0$ and $1$, inclusive.

Step2: Sum all probabilities

$$0.15 + 0.20 + 0.10 + 0.10 + 0.15 + 0.20 = 1.00$$

Step3: Verify validity

Since all individual probabilities are in $[0,1]$ and their total is $1$, the model satisfies the requirements for a valid probability model.

Answer:

Yes, this is a valid probability model.