A card is selected from a pack of 52 cards,How many points are there i

1.	A card is selected from a pack of 52 cards,How many points are there in the sample space? (b) Calculate the probability that the card is an ace of spades, (c) Calculate the probability that the card is (i) an ace (ii) black card.
Answer» We have, number of possible outcomes = 52 n(S) = 52= ⁵²C₁ (a) There are 52 points in the sample – space. (b) Let A: ‘a selected card is an ace of spades’ Clearly the number of elements in the set A is 1. i.e., n(A) =¹C₁ ∴ Required probability = P(A) = n(A)/n(S) = 1/52 (c) (i) Let B: ‘a selected card is an ace’ we know that, in a deck of 52 cards, there are 4 different aces. ∴ n(B) = 4= ⁴C₁ ∴ Required probability = P(B) = n(B)/n(S) = 4/52 = 1/13 (ii) Let C: ‘a selected card is black’ There are 26 black cards in a pack o f 52 cards ∴ n(C) = ²⁶C₁ = 26 ∴ Required probability = P(C) = n(C)/n(S) = 26/52 = 1/2

A card is selected from a pack of 52 cards,How many points are there in the sample space? (b) Calculate the probability that the card is an ace of spades, (c) Calculate the probability that the card is (i) an ace (ii) black card.

Answer»

We have, number of possible outcomes = 52 n(S) = 52= ⁵²C₁

(a) There are 52 points in the sample – space.

(b) Let A: ‘a selected card is an ace of spades’

Clearly the number of elements in the set A is 1. i.e., n(A) =¹C₁

∴ Required probability

= P(A) = n(A)/n(S) = 1/52

∴ n(B) = 4= ⁴C₁

∴ Required probability

= P(B) = n(B)/n(S) = 4/52 = 1/13

(ii) Let C: ‘a selected card is black’ There are 26 black cards in a pack o f 52 cards

∴ n(C) = ²⁶C₁ = 26

∴ Required probability

= P(C) = n(C)/n(S) = 26/52 = 1/2

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A card is selected from a pack of 52 cards,How many points are there in the sample space? (b) Calculate the probability that the card is an ace of spades, (c) Calculate the probability that the card is (i) an ace (ii) black card.

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