Question

4. Two cards are drawn randomly drawn (without
replacement) from an arbitrary deck of 52 playing cards.
and Y are the number of aces obtained in the first draw
and number of aces drawn in both draws respectively. Fin
(i) the joint probability distribution of X and Y;
(ii) the marginal distribution of X;
(iii) the conditional distribution of Y given X=1;
(iv) P(X+Y< 4);
(v) P(X+Y = 6/Y=3).​

Answer 1

Probability of getting an ace on both draws = 0.0045

Step-by-step explanation:

There are 52 cards in total.

Number of aces = Y = 4

Let P(A) be the probability of getting an ace in the first draw.

P(A) = 4/52 = 1/13

Let P(B) be the probability of getting an ace in the second draw.

If the card is not replaced,

then P(B) = 3/51

Probability of getting an ace on both draws = P(A) * P(B)

= 1/13 * 3/51

= 3/663

= 1/221

= 0.0045