Below, a two-way table is given
for student activities.
Sports Drama Work Total
7
3
2
5
Sophomore 20
Junior
20
Senior
25
Total
13
5
Find the probability the student is in drama,
given that they are a sophomore.
P(drama | sophomore) = P(drama and sophomore) [?]%
P(sophomore)
Round to the nearest whole percent.
=
Answers
The probability that a student is in drama, given that they are a sophomore, is approximately 47%.
To calculate the probability that a student is in drama, given that they are a sophomore, we need to use Bayes' theorem:
P(drama | sophomore) = P(drama and sophomore) / P(sophomore)
From the given table, we can see that there are 3 sophomores in drama, out of a total of 20 sophomores:
P(drama and sophomore) = 3/20
And there are a total of 20 sophomores:
P(sophomore) = 20/63
Therefore, we can calculate:
P(drama | sophomore) = (3/20) / (20/63) = 0.4725
Rounding to the nearest whole percent, we get:
P(drama | sophomore) ≈ 47%
So the probability that a student is in drama, given that they are a sophomore, is approximately 47%.
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