Probability Question 7

Question

an experiment consists of dealing 5 cards from a standard 52 card deck what is the probability of being dealt a 10 jack queen king ace all in the same suit?

round to 7 decimal places

Answer 1

The probability of being dealt a 10, J, Q, K, or A in any suit on the first card is 20/52 (5 cards * 4 suits).  Once you have one card and a suit, the odds start going down:

 

1st card = 20/52

2nd card = 4/51   (4 cards in the sequence left in that suit out of 51 cards left)

3rd card = 3/50    (3 cards in the sequence left in that suit out of 50 cards left)

4th card = 2/49    (2 cards in the sequence left in that suit out of 49 cards left)

5th card = 1/48    (1 cards in the sequence left in that suit out of 48 cards left)

 

The odds of being dealt all 5 = (20/52)*(4/51)*(3/50)*(2/49)*(1/48) = 1.54*10^-6