Question

Cards, marked with numbers 5 to 50, are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is (i) a prime number less than 10 (ii) a perfect square.

Answer 1

All possible outcomes are 5, 6, 7, 8...................50.

Number of all possible outcomes = 46

(i) Out of the given numbers, the prime numbers less than 10 are 5 and 7.
Let E₁ be the event of getting a prime number less than 10.
Then, number of favourable outcomes = 2​
∴ P (getting a prime number less than 10) = $\frac{2}{46}=\frac{1}{23}$

(ii) Out of the given numbers, the perfect squares are 9, 16, 25, 36 and 49.
Let E₂ be the event of getting a perfect square.
Then, number of favourable outcomes = 5​
∴ P (getting a perfect square) = $\frac{5}{46}$