Question

Mickey keeps picking playing cards out of a standard deck of 52 cards, hoping that she will

draw a diamond. There are 13 diamonds in the deck. After looking at each card, she places it
back in the deck. What is the probability that Mickey will draw her first diamond on the 8th
attempt?
O 3%
05%
06%
O 8%

Answer 1

03%

Explanation:

In this situation Mickey should have drew first 7 cards that are not diamond and then on the 8th attempt she should draw an ace.

Let A be the event of drawing 7 cards which are not diamond and B the event of drawing an ace card. therefore required probability is P(A∩B)=P(A)*P(B)

Now, there are 13 diamonds and 39 other cards. Hence,

P(A)=(
`(39)/(52)`)⁷=0.1335

After drawing 7 non-diamond cards, the 8th card must be a diamond.Hence,

P(B)=
`(13)/(52)`=0.25

Hence, P(A∩B)=P(A)*P(B)=0.1335*0.25=0.033(approximately 0.03,i.e. 3%)

Therefore probability that Mickey will draw her first diamond on the 8th

attempt is 3%