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
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- 3 cards are drawn, thus [tex]n = 3[/tex].
- In a deck of 52 cards, 12 are faces, thus [tex]p = \frac{12}{52} = 0.2308[/tex].
The probability of at least one face is given by:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.2308)^{0}.(0.7692)^{3} = 0.455[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.455 = 0.545[/tex]
0.545 = 54.5% probability that of the 3 cards drawn, at least 1 is a face card.
A similar problem is given at https://brainly.com/question/24863377
