[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.

g. What is the probability that a randomly chosen household has zero televisions? Would this be considered an impossible event?

Verified step by step guidance

1. Identify the probability associated with the event of interest, which is the household having zero televisions. From the table, locate the value of \(P(x)\) when \(x = 0\).
2. Note that the probability for zero televisions is given as \(P(0) = 0\). This means the probability of selecting a household with zero televisions is zero.
3. Recall the definition of an impossible event in probability: an event that cannot occur has a probability of zero.
4. Since \(P(0) = 0\), conclude that the event of a household having zero televisions is an impossible event according to this probability distribution.
5. Summarize that the probability is zero and this corresponds to an impossible event in the context of this problem.

Key Concepts

Probability of an Event

The probability of an event is a measure between 0 and 1 that indicates how likely the event is to occur. A probability of 0 means the event cannot happen, while a probability of 1 means it is certain. Probabilities for all possible outcomes in a distribution sum to 1.

Impossible Event

An impossible event is one that has a probability of exactly 0, meaning it cannot occur under the given circumstances. In the context of the table, if the probability of zero televisions is 0, it means no household has zero televisions, making it impossible in this dataset.

Discrete Probability Distribution

A discrete probability distribution lists all possible values of a discrete random variable and their associated probabilities. Each probability corresponds to the chance of that specific value occurring, and the sum of all probabilities equals 1, ensuring a complete description of the variable's behavior.