Two cards are drawn at random from an ordinary deck of playi

Two cards are drawn at random from an ordinary deck of playing card. The first is not replaced before the second is drawn. What is the probability that both cards are red? a) 1/4 b) 25/102 c) 6/13 d) 1/2 Five cards are dealt at random from a deck of 52 playing cards. Find the probability that three of them are sevens. a) ~ 0.01736 b) ~ 0.07971 c) ~ 0.00797 d) ~ 0.00174

Solution

Total number of red cards is 26

So probablity of both cards being red is

(26*25)/(52*51)=25/102

15.

There are a total of 4 sevens

Selecting 3 sevesn in done in C(4,3)=4 ways

Other two can be selected in C(48,2)=48*47/2=1128

So required probablity is

(4*1128)/C(52,5)~0.001736