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?

(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) The outcome of the two cards are independent because the occurrence of one does not affect the occurrence of the other.

b) in a 52 playing cards number of 3 is 4. [n(3)=4] , number of 10 is 4 [n(10)=4]

P(3) * p(10) = 4/52 *4/52= 1/13*1/13= 1/169

c) n(10)=4 n(3)=4

P(10) * P(3)= 4/52 * 4/52= 1/13 *1/13= 1/169

d) probability of drawing a 10 and a 3 in either order.

P(10)*P(3) + p(3)*p(10)

1/13 * 1/13 + 1/13 * 1/13

1/169 + 1/169

=2/169