\(A\) and \(B\) are two candidates seeking admission in a college. The probability that \(A\) is selected is…
\(A\) and \(B\) are two candidates seeking admission in a college. The probability that \(A\) is selected is 0.7 and the probability that exactly one of them is selected is \(\mathbf{0 . 6}\). Find the probability that \(B\) is selected.
0.15
0.20
0.25
0.30
Solution
Given, \(P(A)=0.7\)
Probability of exactly one of them is selected \(=0.6\)
\(\begin{gathered}
P[(\overline{\mathrm{A}} \cap \mathrm{B}) \cup(\mathrm{A} \cap \overline{\mathrm{B}})]=0.6 \\
P(A)+P(B)-2 P(A \cap B)=0.6 \\
0.7+P(B)-2 P(A) \cdot P(B)=0.6 \\
{[\because A, B \text { are independent events }]} \\
P(B)-2 \cdot(0.7) P(B)=0.6-0.7 \\
P(B)-\frac{7}{5} P(B)=-0.1 \\
\frac{-2}{5} P(B)=\frac{-1}{10} \\
P(B)=\frac{1}{4} \Rightarrow P(B)=0.25
\end{gathered}\)
Hence, option (c) is correct.