✓ Board-verified
Mathematics · 2023 · 4 marks
CBSE 2023 · Region 2 · Set 2 · Q36
Recent studies suggest that roughly 12 % of the world population is left handed. Depending upon the parents, the chances of having a left handed…
Recent studies suggest that roughly $\displaystyle 12 \%$ of the world population is left handed.
Depending upon the parents, the chances of having a left handed child are as follows: A : When both father and mother are left handed : Chances of left handed child is $\displaystyle 24 \%$. B : When father is right handed and mother is left handed : Chances of left handed child is $\displaystyle 22 \%$. C : When father is left handed and mother is right handed : Chances of left handed child is $\displaystyle 17 \%$. D : When both father and mother are right handed : Chances of left handed child is $\displaystyle 9 \%$. Assuming that $\displaystyle \mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})=\mathrm{P}(\mathrm{C})=\mathrm{P}(\mathrm{D})=\frac{1}{4}$ and L denotes the event that child is left handed. Based on the above information, answer the following questions :
(i)
Find $\displaystyle \mathrm{P}(\mathrm{L} / \mathrm{C})$
(ii)
Find $\displaystyle \mathrm{P}(\overline{\mathrm{L}} / \mathrm{A})$
(iii)
(a)
Find $\displaystyle \mathrm{P}(\mathrm{A} / \mathrm{L})$
OR
(b)
Find the probability that a randomly selected child is left handed given that exactly one of the parents is left handed.
Marking-scheme solution
(i)
$\displaystyle \mathbf{P}(\mathbf{L} \mid \mathbf{C})=\frac{\mathbf{1 7}}{\mathbf{1 0 0}}$
(ii)
$\displaystyle \mathbf{P}(\overline{\mathbf{L}} \mid \mathbf{A})=\mathbf{1}-\mathbf{P}(\mathbf{L} \mid \mathbf{A})=\mathbf{1}-\frac{\mathbf{2 4}}{\mathbf{1 0 0}}=\frac{\mathbf{7 6}}{\mathbf{1 0 0}}$ or $\displaystyle \frac{\mathbf{1 9}}{\mathbf{2 5}}$
(iii)
$\displaystyle \mathrm{P}(\mathrm{A} \mid \mathrm{L})=\frac{\dfrac{1}{4} \times \dfrac{24}{100}}{\dfrac{1}{4} \times \dfrac{24}{100}+\dfrac{1}{4} \times \dfrac{22}{100}+\dfrac{1}{4} \times \dfrac{17}{100}+\dfrac{1}{4} \times \dfrac{9}{100}}=\frac{24}{72}=\frac{1}{3}$
Or
Probability that a randomly selected child is left-handed given that exactly one of the parents is left handed
$\displaystyle =\mathbf{P}(\mathbf{L} \mid \mathbf{B} \cup \mathbf{C})=\frac{\mathbf{2 2}}{\mathbf{1 0 0}}+\frac{\mathbf{1 7}}{\mathbf{1 0 0}}=\frac{\mathbf{3 9}}{\mathbf{1 0 0}}$
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 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.