Question

the owner of a local movie theater keeps track of the number of tickets sold in each purchase. the owner determines the probabilities based on these records. let x represent the number of tickets bought in one purchase. the distribution for x is given in the table. which of the following correctly represents the probability of a randomly selected purchase having at most three tickets? p(x ≤ 3) p(x < 3) p(x ≥ 3) p(x > 3)

Explanation:

The phrase "at most three" means three or less. In probability notation, if \(X\) represents the number of tickets, then \(X\leq3\) means the value of \(X\) can be 1, 2, or 3. The probability of \(X\) being at most three is written as \(P(X\leq3)\).

• \(P(X < 3)\) means the probability that \(X\) is less than 3 (i.e., \(X = 1\) or \(X=2\)), which is not the same as "at most three".
• \(P(X\geq3)\) means the probability that \(X\) is 3 or more (i.e., \(X = 3\), \(X = 4\), or \(X=5\)).
• \(P(X>3)\) means the probability that \(X\) is greater than 3 (i.e., \(X = 4\) or \(X = 5\)).

Answer:

\(P(X\leq3)\)