What is the probability of drawing a spade each time a card is drawn from a deck of 52 cards 3 times, if replacement occurs each time? a. 648-13-05-00-00_files/i0090000.jpg c. 648-13-05-00-00_files/i0090001.jpg b. 648-13-05-00-00_files/i0090002.jpg d. 648-13-05-00-00_files/i0090003.jpg

Question

anonymous · Answer

In the 52 cards, the jokers are already excluded from the deck. Also the kind of spades in the 52 cards is one of 4 kinds in the cards, namely an 1/4 of 52. Then the 52 cards include 52*0.25 = 13 spade cards. And the probability to draw a spade card is 13/52.
The challenge is to be found the probability to draw a spade card 3 times when the replacement occurs each time. Therefore, according to the Multiplication Rule to have a spade card every single time of drawing, it has to multiply the probabilities of every single event of spade's card drawing in these 3 times. Namely the requested probability is : (13/52)* (13/52)* (13/52) = 0.015625  or 1.5%.