Question

60 juniors and sophomores were asked whether or not they will attend the prom this year. The data from the survey is shown in the table. Find P(will attend the prom|sophomore).

Attend the prom Will not attend the prom Total
Sophomores 10 17 27
Juniors 24 9 33
Total 34 26 60

Answer 1

The probability of a sophomore attending the prom, given that they were selected from the group of sophomores, is:

P(will attend the prom|sophomore) = (number of sophomores attending the prom) / (total number of sophomores)

From the table, we see that the number of sophomores attending the prom is 10, and the total number of sophomores is 54 (10 + 17 + 27). Therefore:

P(will attend the prom|sophomore) = 10 / 54

Simplifying the fraction, we get:

P(will attend the prom|sophomore) = 5 / 27

So the probability of a sophomore attending the prom is 5/27 (18.519%).