Amagician 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. two additional people do the same. find the probability that of the 3 cards drawn, at least 1 is a face card. (round your answer to one decimal place.)

Using the binomial distribution, it is found that there is a 0.545 = 54.5% probability that of the 3 cards drawn, at least 1 is a face card.

For each card drawn, there are only two possible outcomes, either it is a face card, or it is not. The probability of a card being a face card is independent of any other card, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

The parameters are:

In this problem:

The probability of at least one face is given by:

In which:

Then:

0.545 = 54.5% probability that of the 3 cards drawn, at least 1 is a face card.

A similar problem is given at link

0.54

Step-by-step explanation:

We know that there are 12 face cards out of the 52 cards of a standard deck. So the probability of drawing a face card will be:  

Logically the probability of not drawing a face card will be:  

Since the drawn cards by audience member are put back in the deck, each draw is independent from the previous draw.  

Therefore, the probability that of the 3 cards drawn, no card is  is a face card is given by :

Now, the probability that of the 3 cards drawn,  at least 1 is a face card is given by :-

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

idk

step-by-step explanation: