Correct Answer - Option 4 : 1/221
Given:
Two cards are randomly drawn from a pack of 52 cards.
Formula Used:
The probability of occurrence of an event E, within a sample space S, is given by:
P(E) = n(E) / n(S)
where P(E) = probability of occurrence of the event E,
n(E) = number of times the event E occurs, and
n(S) = number of points in the sample space S.
Calculation:
We know that the number of aces in a pack of 52 cards = 4 (one heart, one spade, one diamond, and one club)
Total number of cards = 52,
Number of cards drawn = 2
∴ n(S) = 52C2 = 1326
Also, the maximum possible number of ways of drawing any two out of the four aces = 4C2
∴ n(E) = 4C2 = 6
∴ P(E) = 6/1326 = 1/221
∴ The probability that both the cards are aces when two cards are drawn at random from a pack of 52 cards, is 1/221
