Question

you draw two cards from a standard deck of 52 cards and do not replace the first card before you draw a second. What is the probability the first card is a three of spades and the second card is a spade?

Answer 1

Solution:

Total 52 cards

Spade cards 13

In this 13 , a card of "Three of spade"

Consider 2 cards are selected without replacement.

P(1st card is of "Three of spade") = 1/52

Now , 51 cards are remaining. Out of 51 , there are 12 cards of spade

P(Second card is a spade) = 12/51

So ,

Required probability

= P(1st card is of "Three of spade" AND 2nd card is a spade)

= [1/52]*[12/51]

= 12/[52*51]

= 1/221

= 0.00452488687

Answer : Required probability = 1/221 = 0.00452488687