Students in the 7th and 8th grade at Imawinner Middle School are going on a field trip to the planetarium. If a student actively participates in the engagement activities at the planetarium, they are entered into a raffle to win a free lunch from their favorite restaurant. The table below shows the number of students in each grade and homeroom who engaged in the activities.

Homeroom A | Homeroom B | Homeroom C
7th Grade | 8 | 10 | 7
8th Grade | 9 | 10 | 9

What is the probability the winner is NOT in Homeroom B?

1 answer

First, we need to find the total number of students who participated in the engagement activities at the planetarium.
Total number of students in Homeroom A = 8 + 9 = 17
Total number of students in Homeroom B = 10 + 10 = 20
Total number of students in Homeroom C = 7 + 9 = 16

Total number of students who participated = 17 + 20 + 16 = 53

Now, we need to find the number of students who participated in activities but are NOT in Homeroom B. This would be the sum of students from Homeroom A and Homeroom C.
Number of students NOT in Homeroom B = 17 + 16 = 33

Therefore, the probability that the winner is NOT in Homeroom B is:
Probability = Number of students NOT in Homeroom B / Total number of students who participated
Probability = 33 / 53
Probability = 0.6226 or 62.26%

Therefore, the probability that the winner is NOT in Homeroom B is 62.26%.