CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Q313 Marksindependent_events
CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Question 31 (Probability)
On a stormy day a sniper is three times as likely to hit as to miss with each shot. For two shots, find the probabilities that (i) the target is hit at least once and (ii) at least one shot misses. OR Mother, father and son line up at random. E is the event that the son is at one end, and F is the event that the father is in the middle. Find P(E | F).
Alternative 1 3 Marks
On a stormy day a sniper is three times as likely to hit as to miss with each shot. For two shots, find the probabilities that (i) the target is hit at least once and (ii) at least one shot misses.
Answer: (i) 15/16. (ii) 7/16, under independence.
- Let p be the miss probability. Then p+3p=1, so the hit and miss probabilities are 3/4 and 1/4.
- Under the independence assumed in the official calculation, the probability of two misses is 1/16 and of two hits is 9/16.
- Take complements to obtain 15/16 and 7/16 respectively.
Alternative 2 3 Marks
Mother, father and son line up at random. E is the event that the son is at one end, and F is the event that the father is in the middle. Find P(E | F).
Answer: 1.
- Condition on the father standing in the middle.
- Only MFS and SFM are possible under that condition. In both the son is at an end.
- Thus P(E | F)=2/2=1.