Question

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.

(a) Are the outcomes on the two cards independent? Why?

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.Yes. The events can occur together.    No. The events cannot occur together.No. The probability of drawing a specific second card depends on the identity of the first card.

(b) Find P(3 on 1st card and 10 on 2nd). (Enter your answer as a fraction.)


(c) Find P(10 on 1st card and 3 on 2nd). (Enter your answer as a fraction.)


(d) Find the probability of drawing a 10 and a 3 in either order. (Enter your answer as a fraction.)

Answer 1

a)

two outcomes will be independent , if outcome of one does not effect other,but

here, cards are drawn without replacement,so, probability of second card get effected,so, answer is

No. The probability of drawing a specific second card depends on the identity of the first card.

b)when first card is drawn , total cards left = 51

Find P(3 on 1st card and 10 on 2nd) = P(3 on first)*P(10 on 2nd | 3 on first) = 4/52 * 4/51 = 4/663

c)

P(10 on 1st card and 3 on 2nd) = 4/52 * 4/51 = 4/663

d)

probability of drawing a 10 and a 3 in either order = P(3 on first)*P(10 on 2nd | 3 on first) + P(10 on 1st card and 3 on 2nd) = 4/663 + 4/663 = 8/663