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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 2 · Set 2 · Q29
(a) The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high…
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed.
The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
(i)
target is hit
(ii)
atleast one shot misses the target.
Mother, Father and Son line up at random for a family picture. Let events E : Son on one end and F : Father in the middle. Find P(E/F).
Marking-scheme solution
(i)
Let probability of not hitting $\displaystyle =p$
$\displaystyle \therefore$ Probability of hitting $\displaystyle =3p$
$\displaystyle p+3p=1 \Rightarrow p=\dfrac{1}{4}$
So, Probability of hitting, $\displaystyle P(H)=\dfrac{3}{4}$, Probability of not hitting, $\displaystyle P(\bar{H})=\dfrac{1}{4}$
Now, $\displaystyle P(\text{Target is hit})=1-P(\bar{H}\bar{H})=1-\dfrac{1}{4} \times \dfrac{1}{4}=\dfrac{15}{16}$
(ii)
$\displaystyle P$ (at least one shot misses the target)
$\displaystyle =1-P(HH)=1-\dfrac{3}{4} \times \dfrac{3}{4}=\dfrac{7}{16}$
There are $\displaystyle 3$ people - Mother $\displaystyle (M)$, Father $\displaystyle (F)$, Son $\displaystyle (S)$.
Sample Space $\displaystyle =\{MFS, MSF, FMS, FSM, SMF, SFM\}$
Total possible arrangements $\displaystyle =6$
Given $\displaystyle E$ : Son on one end, $\displaystyle F$ : Father in the middle
$\displaystyle P(E \cap F)=P(\text{Son on one end and Father in the middle})=\dfrac{2}{6}, P(F)=\dfrac{2}{6}$
$\displaystyle \therefore P(E \mid F)=\dfrac{P(E \cap F)}{P(F)}=1$
Alternative Method :
For $\displaystyle P(E \mid F)$, as $\displaystyle F$ has already occured which means that the father is in the middle. So, son has to be on one end.
$\displaystyle \therefore P(E \mid F)=1$ (sure event)
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.