Suppose that 3 cards are drawn from a​ well-shuffled deck of 52 cards. What is the probability that all 3 are not face cards ​?

Question

i am struggling and i really need help finding this answer

Answer 1

So, there are 4 face cards for every suit (dismonds, hearts, etc.) i.e. 4 out of every 13 cards. Since there are 4 suits, the probability of picking a face card (the first time) is 16 / 52 (simplified to 4 / 13).

 

This means the probability of NOT picking a face card the first time is 9 / 13. Keep that number in mind.

 

Now we're left with 1 fewer non-face card, but the face cards are intact. The total has decreased from 52 to 51.

 

So, we go from a probability of 9 / 13 to (51 - 16) / 51 of picking a non-face card = 35 / 51 (2nd time).

 

Now our total reduces to 50 cards. Keep in mind there are still 16 face cards. So, the non-face cards = 50 - 16 = 34.

 

Probability of picking another non-face card = 34 / 50 (simplified to 17 / 25).

 

The probability, therefore, of picking 3 non-face cards =   9   x   35   x   17

                                 13 x  51  x 25

Easy to solve now?