Question

In Class XI of a school 40% of the student's 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.

Answer 1

Let A be the event in which the selected student studies Mathematics and B be the event in which the selected student studies Biology. 

Accordingly,\( P(A) = 40\)% =\(\frac{40}{100}=\frac{2}{5}\)

\(P(B) = 30\)%=\(\frac{30}{100}=\frac{3}{10}\)

\(P(A\) and \(B) = 10\)%=\(\frac{10}{100}=\frac{1}{10}\)

We know that \(P(A\) or \(B) = P(A) + P(B) - P(A\) and \(B)\)

\(∴P(A\) or \(B)\)\(=\frac{2}{5}+\frac{3}{10}-\frac{1}{10}=\frac{6}{10}=0.6\)
Thus, the probability that the selected student will be studying Mathematics or Biology is 0.6.