**Case Study - 2**

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 the card bears an even number, th

Question

**Case Study - 2**

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 the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose.

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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 30?

(iii) (a) What is the probability that Rahul draws a card with a prime number between 50 and 74?

**OR**

(iii) (b) What is the probability that Rahul draws a card with an even number divisible by 5?

Accepted Answer

Step 1: (i) Total possible outcomes $= 74 - 10 + 1 = 65$.
Even numbers from 10 to 74: $10, 12, 14, \ldots, 74$. Number of even numbers $= 33$.
P(even number) $= \frac{33}{65}$
Step 2: (ii) Odd numbers less than 30 from 10 to 74: $11, 13, 15, 17, 19, 21, 23, 25, 27, 29$. Count $= 10$.
P(odd number less than 30) $= \frac{10}{65} = \frac{2}{13}$
Step 3: (iii)(a) Favourable outcomes are $53, 59, 61, 67, 71, 73$. Number of favourable outcomes $= 6$.
P(prime number between 50 and 74) $= \frac{6}{65}$
Step 4: (iii)(b) Favourable outcomes are $10, 20, 30, 40, 50, 60, 70$. Number of favourable outcomes $= 7$.
P(even number divisible by 5) $= \frac{7}{65}$

Question

Solution