Problem

Use the probability distribution to complete parts (a) through (d) below. The probability distribution of number of televisions per household in a small town $\begin{array}{lcccc}\mathbf{x} & 0 & 1 & 2 & 3 \\ \mathbf{P}(\mathbf{x}) & 0.05 & 0.18 & 0.31 & 0.46\end{array}$ (b) Find the probability of randomly selecting a household that has two or more televisions. The probability is 0.77 (Type an integer or a decimal. Do not round.) (c) Find the probability of randomly selecting a household that has between one and three televisions, inclusive. The probability is 0.95 (Type an integer or a decimal. Do not round.) (d) Find the probability of randomly selecting a household that has at most two televisions. The probability is (Type an integer or a decimal. Do not round.)

Solution

Step 1 :The probability distribution of the number of televisions per household in a small town is given as follows: \(\begin{array}{lcccc}\mathbf{x} & 0 & 1 & 2 & 3 \\ \mathbf{P}(\mathbf{x}) & 0.05 & 0.18 & 0.31 & 0.46\end{array}\)

Step 2 :To find the probability of randomly selecting a household that has two or more televisions, we add the probabilities of a household having 2 and 3 televisions. This gives us a probability of 0.77.

Step 3 :To find the probability of randomly selecting a household that has between one and three televisions, inclusive, we add the probabilities of a household having 1, 2, and 3 televisions. This gives us a probability of 0.95.

Step 4 :To find the probability of randomly selecting a household that has at most two televisions, we add the probabilities of a household having 0, 1, or 2 televisions. This gives us a probability of 0.54.

Step 5 :Final Answer: The probability of randomly selecting a household that has at most two televisions is \(\boxed{0.54}\).

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Source: https://solvelyapp.com/problems/17723/

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