Question

A magician shuffles a standard deck of playing cards and allows an audience member to pull out a card, look at it, and replace it in the deck. Three additional people do the same. find the probability that of the four cards drawn at least one is a face card.(Round to one decimal place)

The answer is not 0.5478, its say that the answer is wrong when I put it in.

Answer 1

Since in a deck of cards there is 12 face cards

And this experiment is done with 4 peoples

And it's with replacement as explained in the question

So there is equal chance of getting face card for each one

So probability of getting face card=12÷52=3÷13=3/13

So probability of getting at least one face card so

Here one of them gets face card in 4 ways

2of them gets face card in 6 ways

3 of them gets face card in 4 ways

All gets face card in 1 way

So

Required oprobabilit=4*(3/13)*(10/13)*(10/13)*(10/13)+6*(3/13)*(3/13)*(10/13)*(10/13)+3*(3/13)*(3/13)*(3/13)*(10/13)+(3/13)*(3/13)*(3/13)*(3/13)

=0.4201+0.1891+0.0378+0.0028=0.6498