Let A and B be two independent events such that $\mathrm{P}(\mathrm{A})=\frac{1}{3}$ and $\mathrm{P}(\mathrm{B})=\frac{1}{6}$. Then, which of the following is TRUE?

(C) $P\left(\frac{A}{B^{\prime}}\right)=\frac{1}{3}$

(A) $P\left(\frac{A}{B}\right)=\frac{2}{3}$

(B) $P\left(\frac{A^{\prime}}{B^{\prime}}\right)=\frac{1}{3}$

(D) $P\left(\frac{A}{(A \cup B)}\right)=\frac{1}{4}$

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Probability

Let A and B be two independent events such that

P (A) = \frac{1}{3}

and

P (B) = \frac{1}{6}

. Then, which of the following is TRUE?

Answer: (C)

Because

A

and

B

are independent, so are

A

and

B^{'}

, which means conditioning on

B^{'}

leaves the probability of

A

unchanged:

P (A ∣ B^{'}) = P (A) = \frac{1}{3}

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Single correct option