# Thread: 2 face cards not drawn, with replacement

1. ## 2 face cards not drawn, with replacement

Using a standard deck, find the probability that two face cards are not drawn, with replacement.

My first thought is that this can be done in 3 ways, no face cards, and one face card as either the first or second card drawn.

P(No face cards) = 40/52 * 40/52
P(No face card then a face card)= 40/52 * 12/52
P(Face card then no face card)= 12/52 * 40/52

Add them all up and get 160/169

My second thought is to find the complement.

1 - P(two face cards) = 1 - (12/52 * 12/52)
= 1 - 9/169
= 160/169

I'm thrilled that I got the same number, but I am tired and need someone to check over it... Please and thank you.

2. Originally Posted by tcRom
Using a standard deck, find the probability that two face cards are not drawn, with replacement.

My first thought is that this can be done in 3 ways, no face cards, and one face card as either the first or second card drawn.

P(No face cards) = 40/52 * 40/52
P(No face card then a face card)= 40/52 * 12/52
P(Face card then no face card)= 12/52 * 40/52

Add them all up and get 160/169

My second thought is to find the complement.

1 - P(two face cards) = 1 - (12/52 * 12/52)
= 1 - 9/169
= 160/169

I'm thrilled that I got the same number, but I am tired and need someone to check over it... Please and thank you.
Looks OK. The second method is the best approach.