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Question
A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is divisible by 2 or 3.
Solution
Total number of outcomes = 25
Out of the given numbers, numbers divisible by 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 and 24.
Out of the given numbers, numbers divisible by 3 are 3, 6, 9, 12, 15, 18, 21 and 24.
Out of the given numbers, numbers divisible by both 2 and 3 are 6, 12, 18 and 24.
Number of favourable outcomes = 16
∴ P(getting a card divisible by 2 or 3) = P(E1) = `("Number of outcomes favourable to" E_1)/"Number of all possible outcomes"`
`= 16/25`
Thus, the probability that the number on the drawn card is divisible by 2 or 3 is `16/25`.
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