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 \[ \begin{array}{lcccc} x & 0 & 1 & 2 & 3 \\ P(x) & 0.05 & 0.18 & 0.31 & 0.46 \end{array} \] (a) Find the probability of randomly selecting a household that has one or 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: \[\begin{array}{lcccc} x & 0 & 1 & 2 & 3 \\ P(x) & 0.05 & 0.18 & 0.31 & 0.46 \end{array}\]

Step 2 :We are asked to find the probability of randomly selecting a household that has one or two televisions.

Step 3 :To find this, we need to add the probabilities of a household having one television and a household having two televisions.

Step 4 :The probability of a household having one television, denoted as \(P_1\), is given as 0.18.

Step 5 :The probability of a household having two televisions, denoted as \(P_2\), is given as 0.31.

Step 6 :We add these two probabilities to get the total probability of a household having one or two televisions, denoted as \(P_{1\_or\_2}\).

Step 7 :So, \(P_{1\_or\_2} = P_1 + P_2 = 0.18 + 0.31 = 0.49\).

Step 8 :Final Answer: The probability of randomly selecting a household that has one or two televisions is \(\boxed{0.49}\).

From Solvely APP
Source: https://solvelyapp.com/problems/17719/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download