Question

There are 12 face cards in a deck of standard playing cards and 20 even numbered cards. if you draw one card and look at it. then replace it and then draw another card. what is the probability that you would draw a face card and then an even numbered card?

Answer 1

`(9)/(64)`

Explanation:

There are 12 face cards in a deck of standard playing cards and 20 even numbered cards, in total 32 cards.

1. The probabilty that the first drawn card is face card is

`p_1=(12)/(32)=(3)/(8).`

2. The probabilty that the second drawn card is an even numbered card (even numbered cards are 6, 8, 10 - 12 in total, odd numbered cards are 7, 9 - 8 in total) is

`p_2=(12)/(32)=(3)/(8).`

3. The probability that the first drawn card is a face card and the second drawn card is an even numbered card is

`p_1\cdot p_2=(3)/(8)\cdot (3)/(8)=(9)/(64).`