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you roll a standard die 24 times. Knowing that the event satisfies the requirements for a binomial distribution, find the probability that exactly 4 of the rolls show a 6.

A. 0.167
B. 0.214
C. 0.138
D. 1.000

Respuesta :

Rolling a die has a 1/6 chance for each side.
If a 6 is rolled 4 times in 24 rolls, this is what the probability should be, so the answer is A. 16.7%

The probability is 0.214.

Probability

It is the ratio of the favorable event to the total event.

How to calculate probability?

Rolling dice has a 1/6 chance for each side.

If 6 is rolled 4 times in 24.

[tex]\rm P(x) = \dfrac{n!}{(n-x)!x!}p^{x}q^{n-x}[/tex]

Here,

[tex]p = \dfrac{1}{6} \\q = \dfrac{5}{6} \\n = 24\\x = 4[/tex]

Then

[tex]P(x) = \dfrac{n!}{(n-x)!x!}p^{x}q^{n-x}\\\\P(x) = \dfrac{24!}{(24-4)!4!}\dfrac{1}{6} ^{4}\dfrac{5}{6} ^{24-4}\\\\P(x) = 0.214[/tex]

Thus, the probability is 0.214.

More about the probability link is given below.

https://brainly.com/question/795909