A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that card drawn is:
(i) an ace
(ii) a heart
(iii) black
(iv) either an ace or black.

Answer

N/a

Explanation

No. of ways of drawing a card from 52 cards
`=n(S)=.^(52)C_(1)=52`

(i) No of aces of 52 cards `=4`
`:.` No of favourable ways of drawing an ace `=.^(4)C_(1)=4`
and probability of getting an ace `=4/52=1/13`
(ii) No of hearts in 52 cards `=13`
`:.` No of favourable ways of drawing a heart
`=.^(13)C_(1)=13`
and probability of getting a heart `=13/52=1/4`
(iii) No of black cards in 52 cards `=26`
`:.` No of favourable ways of drawing a black card `=.^(26)C_(1)=26`
and probability of getting a black card `=26/52=1/2`
(iv) No. of aces or black cards in 52 cards
`=26+2=28`
`:.` No. of favourable ways of drawing an ace or balck card `=.^(28)C_(1)=28`
and probability of getting an ace or black card `=28/52=7/13`