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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 2 · Set 1 · Q37
Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If…
Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from $\displaystyle 10$ to $\displaystyle 74$ . Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by $\displaystyle 5$, they win by a big margin. If the number is an odd number less than $\displaystyle 30$, they win by a small margin. And if the number is a prime number between $\displaystyle 50$ and $\displaystyle 74$, they lose.
Answer the following questions if Rahul draws a card today :
(i)
What is the probability that Rahul draws a card with an even number?
(ii)
What is the probability that Rahul draws a card with an odd number less than $\displaystyle 30$ ?
(iii)
(a)
What is the probability that Rahul draws a card with a prime number between $\displaystyle 50$ and $\displaystyle 74$?
OR
(b)
What is the probability that Rahul draws a card with an even number divisible by $\displaystyle 5$ ?
Marking-scheme solution
(i) Total possible outcomes \(\displaystyle =74-10+1=65\)
\[P \text { (even number) }=\frac{33}{65}
\]
(ii) \(\displaystyle \mathrm{P}\) (odd number less than $\displaystyle 30$\(\displaystyle )=\frac{10}{65}\) or \(\displaystyle \frac{2}{13}\)
(iii) (a) Favourable outcomes are $\displaystyle 53$, $\displaystyle 59$, $\displaystyle 61$, $\displaystyle 67$, $\displaystyle 71$, $\displaystyle 73$
Number of favourable outcomes \(\displaystyle =6\)
\[P \text { (prime number between } 50 \text { and } 74 \text { ) }=\frac{6}{65}
\]
(b) Favourable outcomes are $\displaystyle 10$, $\displaystyle 20$, $\displaystyle 30$, $\displaystyle 40$, $\displaystyle 50$, $\displaystyle 60$, $\displaystyle 70$
Number of favourble outcomes \(\displaystyle =7\)
\[P(\text { even number divisble by } 5)=\frac{7}{65}
\]
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