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Question
In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.
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Solution
40% of the students in a school study Mathematics.
∴ Probability of a student studying Mathematics P(M) = `40/100 = 0.4`
30% of the students study Biology.
∴ Probability of a student studying Biology P(B) = `30/100 = 0.3`
∴ 10% of the students study both Mathematics and Biology.
∴ Probability of students taking Mathematics and Biology, P(M ∩ B)
= `10/100`
= 0.1
Now if a student is selected at random, then the probability of that student taking Mathematics or Biology is
P(M ∪ B) = P(M) + P(B) – P(M ∩ B)
= 0.4 + 0.3 – 0.1
= 0.6
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