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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.
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
(b) What is the probability that Rahul draws a card with an even number divisible by $5$?
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
(b) What is the probability that Rahul draws a card with an even number divisible by $5$?
Show SolutionHide Solution↓
(i) Total possible outcomes = $74 - 10 + 1 = 65$
P (even number) = $\frac{33}{65}$
(ii) P (odd number less than $30$) = $\frac{10}{65}$ or $\frac{2}{13}$
(iii) (a) Favourable outcomes are $53, 59, 61, 67, 71, 73$
Number of favourable outcomes = $6$
P (prime number between $50$ and $74$) = $\frac{6}{65}$
OR
(b) Favourable outcomes are $10, 20, 30, 40, 50, 60, 70$
Number of favourble outcomes = $7$
P (even number divisble by $5$) = $\frac{7}{65}$
P (even number) = $\frac{33}{65}$
(ii) P (odd number less than $30$) = $\frac{10}{65}$ or $\frac{2}{13}$
(iii) (a) Favourable outcomes are $53, 59, 61, 67, 71, 73$
Number of favourable outcomes = $6$
P (prime number between $50$ and $74$) = $\frac{6}{65}$
OR
(b) Favourable outcomes are $10, 20, 30, 40, 50, 60, 70$
Number of favourble outcomes = $7$
P (even number divisble by $5$) = $\frac{7}{65}$