Ms. Sushmita went to a fair and participated in a game. The game consisted of a box having number cards with numbers from 01 to 30. The three prizes were as per the given table:

Prize	Number on the card drawn at random is a
Wall clock	perfect square
Water bottle	even number which is also a multiple of 3
Purse	prime number

Find the probability of winning a:

(a) Wall Clock

(b) Water Bottle

(c) Purse

Given,

Total number of outcomes = 30

(a) Given,

Numbers that are perfect squares (between 1 to 30) are 1, 4, 9, 16, 25 (5 numbers).

∴ No. of favourable outcomes = 5 perfect squares

P(perfect square) $=\dfrac{\text{No of favourable outcomes}}{\text{Total number of outcomes}} = \dfrac{5}{30} = \dfrac{1}{6}$.

Hence, probability of numbers that are perfect squares = $\dfrac{1}{6}$.

(b) Given,

Even numbers that are also multiples of 3 (between 1 to 30) are 6, 12, 18, 24, 30 (5 numbers)

∴ No. of favourable outcomes = 5 Even numbers that are also multiples of 3

P(even and multiple of 3) $=\dfrac{\text{No of favourable outcomes}}{\text{Total number of outcomes}} = \dfrac{5}{30} = \dfrac{1}{6}$

Hence, probability of numbers that are multiples of 3 and even number = $\dfrac{1}{6}$.

(c) Given,

Prime numbers (1 to 30) are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (10 numbers)

∴ No. of favourable outcomes = 10 Prime numbers

P(prime)

$=\dfrac{\text{No of favourable outcomes}}{\text{Total number of outcomes}} = \dfrac{10}{30} = \dfrac{1}{3}$

Hence, probability of prime numbers = $\dfrac{1}{3}$.