The probability that a student participates in both sports and drama is .
If and
are any two events, then the probability of the joint event
is given by the following formula:
Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.
Suppose denotes that "a student participates in sports" and
denotes that "a student participates in drama".
So, we have ,
,
.
We want to find the probability that a student participates in both sports and drama i.e., we want to find .
By the above formula, we obtain:
Therefore, the probability that a student participates in both sports and drama is .
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