[NW] [DATA] TelevisionsIn the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.

f. What is the probability that a randomly selected household owns either three or four televisions?

Verified step by step guidance

1. Identify the random variable X, which represents the number of televisions in a household, and the corresponding probabilities P(x) from the given probability distribution table.
2. Understand that the problem asks for the probability that a household owns either 3 or 4 televisions, which means we need to find P(X = 3 or X = 4).
3. Recall that for mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities. So, we use the formula: \(P(X=3 \text{ or } X=4) = P(X=3) + P(X=4)\).
4. From the table, find the values of \(P(X=3)\) and \(P(X=4)\), which are 0.176 and 0.186 respectively.
5. Add these probabilities together to get the total probability: \(P(X=3 \text{ or } X=4) = 0.176 + 0.186\).

Key Concepts

Probability Distribution

A probability distribution lists all possible values of a random variable along with their associated probabilities. The sum of all probabilities must equal 1. It helps in understanding how likely different outcomes are in a random experiment.

Random Variable

A random variable is a numerical outcome of a random phenomenon. In this case, X represents the number of televisions in a household. It can take on discrete values, each with a specific probability.

Addition Rule of Probability

The addition rule states that the probability of either event A or event B occurring is the sum of their individual probabilities, provided the events are mutually exclusive. Here, to find the probability of owning three or four televisions, add P(3) and P(4).