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 choice from the following choices: A) 1 / 2 B) 3 / 4 C) 7 / 8 D) 27 / 32 E) 27 / 64
<gadget id="calculator">52 - 13</gadget>
<output>39</output>

<gadget id="calculator">39 / 52</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) * (3/4)</gadget>
<output>9/16 = around 0.5625</output>

<gadget id="calculator">(9/16) * (3/4)</gadget>
<output>27/64 = around 0.421875</output>

<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?
multiply(multiply(divide(subtract(52, 13), 52), divide(subtract(52, 13), 52)), divide(subtract(52, 13), 52))
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 2 nd 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 e