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. what is the probability that a randomly selected purchase has at least two tickets? 0.28 0.55 0.72 0.83

Explanation:

Step1: Use the complement rule

The probability of an event \(A\) and its complement \(\overline{A}\) satisfies \(P(A)=1 - P(\overline{A})\). Let \(A\) be the event that a purchase has at least two tickets. Then \(\overline{A}\) is the event that a purchase has exactly one ticket.

Step2: Calculate the probability

We know that \(P(X = 1)=0.17\). Using the complement rule \(P(X\geq2)=1 - P(X = 1)\). Substitute \(P(X = 1)\) into the formula: \(P(X\geq2)=1-0.17\).

Answer:

\(0.83\)