Mathematics, 20.09.2019 23:30 zhangyixing1

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.)

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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

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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 n = 3

.In a deck of 52 cards, 12 are faces, thus $p = \frac{12}{52} = 0.2308$ .

The probability of at least one face is given by:

$P(X \geq 1) = 1 - P(X = 0)$

In which:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.2308)^{0}.(0.7692)^{3} = 0.455$

Then:

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.455 = 0.545$

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

Answer from: yungkxng57

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:

$\text{ P(face)}=\frac{12}{52}=\frac{3}{13}$

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

$\text{ P(not face)}=1-\text{ P(face)}=\frac{10}{13}$

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 :

$\text{P(not face card)}=\frac{10}{13}\times\frac{10}{13}\times\frac{10}{13}=\frac{1000}{2197}$

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

$\text{P(atleast one face card)}=1-\text{P(not face card)}=1-\frac{1000}{2197}=\frac{1197}{2197}=0.54483\approx0.54$

Answer from: Quest

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

$4x^2-0x-9$

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

$4x^2-0x-9$

$=4x^2-6x+6x-9\\\\=2x(2x-3)+3(2x-3)\\\\=(2x+3)(2x-3)\\\\=(2x-3)(2x+3)$

therefore, the correct factorization of $4x^2-0x-9$ is (2x-3)(2x+3).

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