Question

1b) Two cards are drawn simultaneously or successively without replacement from a

well-shuffled deck of 52 cards. Find the probability distribution of number of aces

).x( Give a graphical representation of probability distribution

Answer 1

Solution:

Let X denote the number of aces in a sample of 2 cards drawn from a well-shuffled pack of 52 playing cards.

So, X can take the values 0,1 and 2.

Now,

$P(X=0) \\ =P( no\ ace ) =\frac{48}{52} \times \frac{47}{51} \\ =\frac{2256}{2652} =\frac{188}{221}$

$P(X=1) \\ =P(1\ ace ) =\frac{4}{52} \times \frac{48}{51}+\frac{48}{52} \times \frac{4}{51} \\ =\frac{384}{2652} =\frac{32}{221}$

$P(X=2)\\ =P(2\ aces ) =\frac{4}{52} \times \frac{3}{51}\\ =\frac{12}{2652} =\frac{1}{221}\\$

$\text { Thus, the probability distribution of } X \text { is given by }\\$