Question

a group of students enter a baseball game. 14 students buy a hotdog, 10 students buy nachos, 12 students buy popcorn, and 4 students buy pizza. find the probability that a student did not buy nachos. p(not nachos) = ? round your answer to the nearest hundredth.

Explanation:

Step1: Calculate total number of students

First, we need to find the total number of students by adding the number of students who bought each item. So we sum up the number of students who bought hotdogs, nachos, popcorn, and pizza.
The number of students who bought hotdogs is 14, nachos is 10, popcorn is 12, and pizza is 4. So the total number of students \( n = 14 + 10 + 12 + 4 \)
\( n=14 + 10+12 + 4=40 \)

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 the total number of students minus the number of students who bought nachos. Let \( x \) be the number of students who did not buy nachos. Then \( x=n - 10\)
Substituting \( n = 40 \), we get \( x = 40- 10=30 \)

Step3: Calculate the probability

The probability \( P(\text{Not Nachos})=\frac{\text{Number of students who did not buy nachos}}{\text{Total number of students}} \)
So \( P(\text{Not Nachos})=\frac{30}{40} = 0.75\)

Answer:

\( 0.75 \)