Question

a group of students enter a baseball gam14 students buy a hotdog, 10 students buynachos, 12 students buy popcorn, and 4students buy pizza. find the probabilitythat a student did not buy nachos.

Explanation:

Step1: Calculate total number of students

First, we need to find the total number of students. We add the number of students who bought each item: \(14 + 10 + 12 + 4\).
\(14+10 = 24\), \(24 + 12 = 36\), \(36+4 = 40\). So total number of students is \(40\).

Step2: Calculate number of students who did not buy nachos

The number of students who bought nachos is \(10\), so the number of students who did not buy nachos is total students minus students who bought nachos: \(40 - 10 = 30\).

Step3: Calculate the probability

Probability is the number of favorable outcomes (students who did not buy nachos) divided by total number of outcomes (total students). So the probability \(P=\frac{30}{40}\), which simplifies to \(\frac{3}{4}\) or \(0.75\).

Answer:

The probability that a student did not buy nachos is \(\frac{3}{4}\) (or \(0.75\)).