There are 13 clubs in a full deck of 52 cards. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a club, you win. If the card is not a club, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a club, and the point is to measure how many draws it took before the person picked a club and, thereby, won. What is the probability that one will pick the first club on the forth draw or later? Choose the correct answer:  A) 1/2  B) 3/4  C) 7/8  D) 27/32  E) 27/64
Favorable case = the club is picked in the third draw or later   Unfavorable cases = The club is picked in either first draw, second draw or third draws   Probability = Favorable outcomes / Total out comes   Also probability = 1-(Unfavorable outcomes / Total out comes)   Unfavorable case 1: probability of club picked in first draw = 13/52 =1/4   Unfavorable case 2: probability of club picked in Second draw (i.e. first draw is not club)= (39/52)*(13/52) =(3/4)*(1/4)= 3/16   Unfavorable case 3: probability of club picked in Third draw (i.e. first and 2nd draws are not clubs)= (39/52)*(39/52)*(13/52) =(3/4)*(3/4)*(1/4)= 9/64   Total Unfavorable Probability = (1/4)+(3/16)+(9/64) = (16/64)+(12/64)+(9/64)=37/64   i.e., Favorable Probability = 1 - (37/64) = 27/64   Answer: Option 27/64
<result>E</result>
There are 13 clubs in a full deck of 52 cards. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a club, you win. If the card is not a club, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a club, and the point is to measure how many draws it took before the person picked a club and, thereby, won. What is the probability that one will pick the first club on the forth draw or later?