CBSE 2026 · Region 4 · Set 1 · Q31 · 3 marks
In a school, the probability of holding a debate competition is $\displaystyle \frac{1}{3}$ and that of a quiz competition is $\displaystyle \frac{2}{3}$. In the two participating teams, A has $\displaystyle 4$ girls and $\displaystyle 6$ boys and B has $\displaystyle 7$ girls and $\displaystyle 3$ boys. If a debate competition is held, the students are selected from team A and for the quiz competition they are selected from team B. If only two students are to be chosen from the teams, then find the probability that one will be a girl and the other a boy.
Marking-scheme solution
Let D be the event a debate competition is held, Q be the event a quiz competition is held and E be the event that one girl & one boy are chosen.
$\displaystyle P(E \mid D)=2 \times \dfrac{4}{10} \times \dfrac{6}{9}=\dfrac{8}{15}, \quad P(E \mid Q)=2 \times \dfrac{7}{10} \times \dfrac{3}{9}=\dfrac{7}{15}$
Now, $\displaystyle P(E)=\dfrac{1}{3} \times \dfrac{8}{15}+\dfrac{2}{3} \times \dfrac{7}{15}=\dfrac{22}{45}$
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.