✓ Board-verified
Mathematics · 2022 · 2 marks
CBSE 2022 · Region 1 · Set 1 · Q4
Let A and B be two events such that P ( A )=5/8, P ( B )=1/2 and P ( A / B )=3/4. Find the value of P ( B / A ).
Let A and B be two events such that $\displaystyle \mathrm{P}(\mathrm{A})=\frac{5}{8}, \mathrm{P}(\mathrm{B})=\frac{1}{2}$ and $\displaystyle \mathrm{P}(\mathrm{A} / \mathrm{B})=\frac{3}{4}$. Find the value of $\displaystyle \mathrm{P}(\mathrm{B} / \mathrm{A})$.
Marking-scheme solution
\[\begin{aligned}
& P(A / B)=\frac{P(A \cap B)}{P(B)}=\frac{3}{4} \Rightarrow P(A \cap B)=\frac{3}{8} \\
& P(B / A)=\frac{P(B \cap A)}{P(A)}=\frac{\dfrac{3}{8}}{\dfrac{5}{8}}=\frac{3}{5}
\end{aligned}
\]
More from Probability
- Assertion: Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is 1/3. Reason…2023
- If A and B are two events such that P(B)=1/5, P(A ∣ B)=2/3 and P(A ∪ B)=3/5, then P(A) is:2025
- A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances of their manufacturing a defective…2025
- Three friends A, B and C got their photograph clicked. Find the probability that B is standing at the central position, given that A is standing at…2022
- A box has 4 green, 8 blue and 3 red pens. A student picks up a pen at random, checks its colour and replaces it in the box. He repeats this process 3…2025
- Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000…2026
- Let M and N be two events such that P(M)=0.6, P(N)=0.2 and P(M ∩ N)=0.5, then P(M^′ / N^′) is2025
- The probability distribution of a random variable X is: where k is some unknown constant. The probability that the random variable X takes the value…2024
CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.