One card is drawn from a well shuffled deck of 52 cards. If each outco

1.	One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (i) a diamond (ii) not an ace (iii) a black card (i.e., a club or a spade) (iv) not a diamond (v) not a black card.
Answer» When a card is drawn from a well shuffled deck of 52 cards, the number of possible outcomes is 52. (i) Let A : ‘the card drawn is a diamond’ Clearly the number of elements in set A is 13. ∵ n(S) = 52 and n(A) = 13 ∴ P(A) = n(A)/n(S) = 13/52 = 1/4 (ii) Let B: ‘card drawn is an ace’. B’: ‘card drawn is not an ace’ we have, n(13) = 4,n(S)= 52 ∴ P(B) = n(B)/n(S) = 4/52 = 1/13 Required probability =P(B’) We have P(B') = 1 - P(B) = 1 - 1/13 = 12/13 (iii) Let C : ‘card drawn is black card’. ∴ Number of elements in set C = 26 i.e., n(C) =26 ∴ P(C) = n(C)/n(S) = 26/52 = 1/2 (iv) Let A: ‘card drawn is a diamond’ ∴ A’: card drawn is not a diamond’ We have n(A) = 13, n(S) = 52 ∴ P(A) = 13/52 = 1/4 we have P(A') = 1 - P(A) = 1 - 1/4 = 3/4 (v) We have p(C) = 1/2 (from (iii)) ∴ P(C') = 1 - P(C) = 1 - 1/2 = 1/2

One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (i) a diamond (ii) not an ace (iii) a black card (i.e., a club or a spade) (iv) not a diamond (v) not a black card.

Answer»

When a card is drawn from a well shuffled deck of 52 cards, the number of possible outcomes is 52.

(i) Let A : ‘the card drawn is a diamond’

Clearly the number of elements in set A is 13.

∵ n(S) = 52 and n(A) = 13

∴ P(A) = n(A)/n(S) = 13/52 = 1/4

(ii) Let B: ‘card drawn is an ace’. B’: ‘card drawn is not an ace’ we have, n(13) = 4,n(S)= 52

∴ P(B) = n(B)/n(S) = 4/52 = 1/13

Required probability =P(B’)

We have P(B') = 1 - P(B) = 1 - 1/13 = 12/13

(iii) Let C : ‘card drawn is black card’.

∴ Number of elements in set C = 26 i.e., n(C) =26

∴ P(C) = n(C)/n(S) = 26/52 = 1/2

(iv) Let A: ‘card drawn is a diamond’

∴ A’: card drawn is not a diamond’

We have n(A) = 13, n(S) = 52

∴ P(A) = 13/52 = 1/4

we have P(A') = 1 - P(A) = 1 - 1/4 = 3/4

(v) We have p(C) = 1/2 (from (iii))

∴ P(C') = 1 - P(C) = 1 - 1/2 = 1/2