A box contains 15 cards numbered 1, 2, 3, …., 15 which are mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is :
(i) odd
(ii) prime
(iii) divisible by 3
(iv) divisible by 3 and 2 both
(v) divisible by 3 or 2
(vi) a perfect square number.

Question

A box contains 15 cards numbered 1, 2, 3, …., 15 which are mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is :
(i) odd
(ii) prime
(iii) divisible by 3
(iv) divisible by 3 and 2 both
(v) divisible by 3 or 2
(vi) a perfect square number.

KnowledgeBoat · Accepted Answer

(i) Let E₁ be the event of choosing an odd number card. E₁ = {1, 3, 5, 7, 9, 11, 13, 15}. ∴ The number of favourable outcomes to the event E₁ = 8. Hence, the probability of choosing an odd number card is . (ii) Let E₂ be the event of choosing a prime number card. E₂ = {2, 3, 5, 7, 11, 13}. ∴ The number of favourable outcomes to the event E₂ = 6. Hence, the probability of choosing a prime number card is . (iii) Let E₃ be the event of choosing card with number that is divisible by 3. E₃ = {3, 6, 9, 12, 15}. ∴ The number of favourable outcomes to the event E₃ = 5. Hence, the probability of choosing a card with number that is divisible by 3 is . (iv) Let E₄ be the event of choosing card with number that is divisible by 3 and 2. E₄ = {6, 12}. ∴ The number of favourable outcomes to the event E₄ = 2. Hence, the probability of choosing a card with number that is divisible by 3 and 2 is . (v) Let E₅ be the event of choosing card with number that is divisible by 3 or 2. E₅ = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15}. ∴ The number of favourable outcomes to the event E₅ = 10. Hence, the probability of choosing a card with number that is divisible by 3 or 2 is . (vi) Let E₆ be the event of choosing card with perfect square number. E₆ = {1, 4, 9}. ∴ The number of favourable outcomes to the event E₆ = 3. Hence, the probability of choosing a card with perfect square number is .

Mathematics

A box contains 15 cards numbered 1, 2, 3, …., 15 which are mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is :
(i) odd
(ii) prime
(iii) divisible by 3
(iv) divisible by 3 and 2 both
(v) divisible by 3 or 2
(vi) a perfect square number.

Probability

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Probability

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