Question

Draw 3 cards without replacement (in other words, draw the top 3 cards from a shuffled deck), repeat this 10 times (for fairness you should reshuffle the cards between each set of 3 cards).

Calculate the theoretical probability of getting the following:

1) P(All 3 cards are spades)

2) P(All 3 cards are Face cards AND clubs)

Answer 1

1)

As we have to calculate no. of ways of pulling out 3 spade cards out of 13, no. of ways = 13C3

Total probability = 52C3

P(All 3 cards are spades)= 13C3/52C3= 286/22100

2)There are 13 club cards in a deck of 52 cards, and 3 of these 13 cards are face cards, which are Queen, King and Joker,

As we have to find no. of ways of pulling these 3 face spade cards out of the 3 face spade cards; 3C3 is no. of ways

P(All 3 cards are Face cards AND clubs)= 3C3/52C3=1/22100