(Q20) 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.

Solution : : 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 =

The number of possible outcomes =

Therefore, P(E) =
=
1

(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 =

Therefore, P(E) =
48
 =
12
Alternate Method :

Note that F is nothing but Ē.

Therefore, we can also calculate P(F) as follows:

P(F) = P(Ē) = 1 - P(E) = 1 -
1
 =