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A box contains 36 cards, bearing only one number from 1 to 36 on each. If one card is drawn at random, find the probability of an event that the card drawn bears, a number divisible by 3 - Algebra

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Sum

A box contains 36 cards, bearing only one number from 1 to 36 on each. If one card is drawn at random, find the probability of an event that the card drawn bears, a number divisible by 3

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Solution

Sample space,

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12, 13, 14, 15, 16, 17, 18, 19, 20,

21, 22, 23, 24, 25, 26, 27, 28, 29, 30,

31, 32, 33, 34, 35, 36}

∴ n(S) = 36

Let C be the event that the card drawn bears a number divisible by 3.

∴ C = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}

∴ n(C) = 12

∴ P(C) = `("n"("C"))/("n"("S"))`

∴ P(C) = `12/36`

∴ P(C) = `1/3`

Concept: Probability of an Event
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