One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will
(i) be an ace, (ii) not be an ace
Well-shuffling ensures equally likely outcomes.
(i) There are 4 aces in a deck. Let E be the event ‘the card is an ace’.
The number of outcomes favourable to E = 4
The number of possible outcomes = 52
Therefore, P(E) = 4/52 = 1/13
(ii) Let F be the event ‘card drawn is not an ace’.
The number of outcomes favourable to the event F = 52 – 4 = 48
The number of possible outcomes = 52
Therefore,
P(E)=48/52=12/13
There are 4 suits in a pack of 52 cards
13- Heart
13- Diamond
13- Spades
13- Clubs
Each suit has one ace, 1jack, 1king, 1queen
So total ace cards = 4
(i) The probability of getting an Ace = 4/52
(ii) There are 48 cards which are not ace
The probability of not getting an Ace = 48/52