KCET · Maths · Probability
Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is \(\frac{2}{5}\). If she visits temple \(A, \frac{1}{3}\) is the probability that she meets her friend, whereas it is \(\frac{2}{7}\) if she visits temple \(B\). Meera met her friend at one of the two temples. The probability that she met her at temple B is
- A \(\frac{7}{16}\)
- B \(\frac{5}{16}\)
- C \(\frac{3}{16}\)
- D \(\frac{9}{16}\)
Answer & Solution
Correct Answer
(D) \(\frac{9}{16}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{P}(\mathrm{A})=\frac{2}{5} \quad \mathrm{~F}: \text { The events of meera meets her friend. } \\ & \mathrm{P}(\mathrm{F} / \mathrm{A})=\frac{1}{3} \\ & \mathrm{P}(\mathrm{F} / \mathrm{B})=\frac{2}{7} \\ & \mathrm{P}(\mathrm{B})=1-\mathrm{P}(\mathrm{A}) \\ & =1-\frac{2}{5} \\ & =\frac{3}{5}\end{aligned}\)
The probability she meet her at temple B
\(\begin{aligned} & P(B / F)=\frac{P(F \cap B)}{P(F)} \\ & =\frac{P(B) \times P(B / F)}{P(A) P(F / A)+P(B) P(B / F)} \\ & =\frac{3 / 5 \times 2 / 7}{(2 / 5 \times 1 / 3)+(3 / 5 \times 5 / 7)}=\frac{9}{16}\end{aligned}\)
The probability she meet her at temple B
\(\begin{aligned} & P(B / F)=\frac{P(F \cap B)}{P(F)} \\ & =\frac{P(B) \times P(B / F)}{P(A) P(F / A)+P(B) P(B / F)} \\ & =\frac{3 / 5 \times 2 / 7}{(2 / 5 \times 1 / 3)+(3 / 5 \times 5 / 7)}=\frac{9}{16}\end{aligned}\)
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