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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 3 · Set 1 · Q6
A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the number 5 has appeared on…
A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the number $\displaystyle 5$ has appeared on atleast one die. $\displaystyle 2$
OR The probability that A hits the target is $\displaystyle \frac{1}{3}$ and the probability that B hits it, is $\displaystyle \frac{2}{5}$. If both try to hit the target independently, find the probability that the target is hit. $\displaystyle 2$ of $\displaystyle 8$
Marking-scheme solution
(a)
$\displaystyle A$: sum is $\displaystyle 7$
$\displaystyle B$: $\displaystyle 5$ has appeared at least on one die
$\displaystyle A \cap B = \{(2,5), (5,2)\}$
\[P\left(\frac{B}{A}\right) = \frac{P(A \cap B)}{P(A)} = \frac{2/36}{6/36} = \frac{1}{3} \]
OR
(b)
$\displaystyle E_1 = A$ hits the target
$\displaystyle E_2 = B$ hits the target
P(target is hit) = $\displaystyle 1$ – P(target is not hit)
\[= 1 - \left(\frac{2}{3} \cdot \frac{3}{5}\right) = \frac{3}{5} \]
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