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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 2 · Set 1 · Q4
A pair of dice is thrown. It is given that the sum of numbers appearing on both dice is an even number. Find the probability that the number…
A pair of dice is thrown. It is given that the sum of numbers appearing on both dice is an even number. Find the probability that the number appearing on at least one die is 3.
Marking-scheme solution
A: number appearing on at least one die is $\displaystyle 3$
B: sum of numbers appearing on both dice is even
Clearly, \(\displaystyle A \cap B=\{(3,1),(3,5),(1,3),(5,3),(3,3)\}\)
\[\begin{aligned}
P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)} & =\frac{5 / 36}{18 / 36} \\
& =\frac{5}{18}
\end{aligned}
\]
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