Question

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distnbution of the number of spade cards.

Answer 1

Let X denote the number of spades in a sample of 2 drawn cards from a well shuffle pack of 52 cards.

Then, X can take the values 0, 1, 2.

Now, P(X = 0) = P(no spade)

= `(""^39C_2)/(""^52C_2)`

= `741/1326`

= `19/34`

P(X = 1) = P(one spade card)

= `(""^13C_1 xx ""^39C_1)/(""^52C_2)`

= `507/1326`

= `13/34`

P(X = 2) = P(both cards are spade)

 = `(""^13C_2)/(""^52C_2)`

= `78/1326`

= `1/17`

Thus, the probability distribution of X is given by

X	P(X)
0	`19/34`
1	`13/34`
2	`1/17`