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
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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) $=\frac{\text{No of favourable outcomes}}{\text{Total number of outcomes}} = \frac{5}{30} = \frac{1}{6}$.
Hence, probability of numbers that are perfect squares = $\frac{1}{6}$.
(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) $=\frac{\text{No of favourable outcomes}}{\text{Total number of outcomes}} = \frac{5}{30} = \frac{1}{6}$
Hence, probability of numbers that are multiples of 3 and even number = $\frac{1}{6}$.
(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)
$=\frac{\text{No of favourable outcomes}}{\text{Total number of outcomes}} = \frac{10}{30} = \frac{1}{3}$
Hence, probability of prime numbers = $\frac{1}{3}$.