A card is drawn from a well shuffled deck of 52 cards. Find the probability that the card drawn is
(i) An ace of hearts
(ii) A black card
(iii) Not a black card
(iv) A king

Explanation

When a card is drwan out of a deck of 52 cards, then the total number of possible outcome is 52
(i) Let A be the event getting an ace of hearts
Clearly, the set A contians only 1 sample point
`therefore P(A)=(1)/(52)`
(ii) Let B be the event getting a black card
Now, set B contains 26 sample points are there are 26 black cards.
`therefore P(B)=(26)/(52)=(1)/(2)`
(iii) We have assumed that the event getting a black card is B, therefore card drawn is not a black card should be B'
We know that P(B') = 1 - P(B)
= `1-(1)/(2)=(1)/(2)
`therefore P(B') = (1)/(2)`
(iv) Let C be the event card drawn is a king
There are 4 sample points in the set C.
`therefore P(C) = (4)/(52)=(1)/(13) " "` { `therefore` are 4 kings in the deck of 52 cards}