Question

# In a group of 50 students, 40 study Mathematics, 32 study Physics, and each student studies at least one of these subjects. a. Use a Venn diagram to find how many students study both subjects. b. If a student from this group is randomly selected, find the probability that he or she: i. studies Mathematics but not Physics ii. studies Physics given that he or she studies Mathematics.

Solution

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a. Say there are $m$ students who study only mathematics, $p$ students who study only physics, and $b$ students who study both the subjects. Then, we are given that,

$m+b = 40, \quad p+b = 32, \quad m+p+b = 50.$

Then, $p = 50 - 40 =10$, and, $m = 50 - 32=18$.

Hence, $b = 50-(10+18) = 22$. The following Venn diagram illustrates the situation.

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