‹ PrevQuestion 111 / 111 · latest first
✓ Board-verified
Mathematics · 2022 · 4 marks
CBSE 2022 · Region 4 · Set 3 · Q14
In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth 10 points and rest of the rings are allotted points 9…
In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth $\displaystyle 10$ points and rest of the rings are allotted points $\displaystyle 9$ to $\displaystyle 1$ in sequential order moving outwards. Archer A is likely to earn $\displaystyle 10$ points with a probability of $\displaystyle 0 \cdot 8$ and Archer B is likely the earn $\displaystyle 10$ points with a probability of $\displaystyle 0 \cdot 9$.
Based on the above information, answer the following questions : If both of them hit the Archery target, then find the probability that
(a)
exactly one of them earns $\displaystyle 10$ points.
(b)
both of them earn $\displaystyle 10$ points.
Marking-scheme solution
$\displaystyle P(A) = 0\cdot8$ , $\displaystyle P(B) = 0\cdot9$
(a)
$\displaystyle P$ (exactly one of them earns $\displaystyle 10$ points) $\displaystyle = P(A)P(\bar{B}) + P(\bar{A})P(B)$
\[= 0\cdot8 \times 0\cdot1 + 0\cdot2 \times 0\cdot9\]
\[= 0\cdot26\]
(b)
$\displaystyle P(A \cap B) = P(A)P(B)$
\[= 0\cdot8 \times 0\cdot9\]
\[= 0\cdot72\]
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.