Question

a survey of all students at a large high school revealed that, in the last month, 38% of them had dined at taco bell, 16% had dined at chipotle, and 9% had dined at both. suppose we select a student at random.
whats the probability that the student has dined at taco bell or chipotle in the last month?
(round to 2 decimal places. leave your answer in decimal form.)

Explanation:

Step1: Use the formula for the probability of \(A\cup B\)

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that a student dined at Taco Bell and \(B\) be the event that a student dined at Chipotle. We are given \(P(A) = 0.38\), \(P(B)=0.16\), and \(P(A\cap B)=0.09\).

Step2: Substitute the values into the formula

Substitute the values into \(P(A\cup B)\):
\(P(A\cup B)=0.38 + 0.16-0.09\)
\(P(A\cup B)=0.45\)

Answer:

\(0.45\)