Suppose that two cards are drawn without replacement from a

Suppose that two cards are drawn without replacement from a well-shuffled deck. What is the probability that both cards have numbers and that the numbers on the cards are the same?

(Note that only the numbers 2 through 10 are shown on cards, since aces, kings, queens, and jacks are represented by letters).

Solution

Total number of cards in a deck = 52.

Total number of cards with numbers = 36

Types of Numbers in cards = 9

Number of cards having same number = 4

Sample space will contain number of possible ways two cards can be selected randomly from the deck without replacement. Sample space = C(52,2)

Favourable cases will contain the number of possible ways of selecting two cards with same numbers .

Favourable cases = C(9,1)*C(4,2)

Let P denote the probability that both cards have numbers and that numbres on the cards are same.

P = ( C(9,1)*C(4,2) )/C(52,2) = 9/221 = 0.0407