Ms. Smith puts a variety of wrapped

chocolate candies into a bag. There are 5

silver-wrapped candies, I purple-wrapped

candy, 2 striped candies, and 4 gold-wrapped

candies. If 15 students select one candy at a

time out of the bag and replace the candy

after each draw, how many students would be

expected to select a gold-wrapped candy

from the bag?

A. 4 students B. 5 students

C. 15 students D. 60 students

Question

10-01-2022
Mathematics

contestada

Ms. Smith puts a variety of wrapped

chocolate candies into a bag. There are 5

silver-wrapped candies, I purple-wrapped

candy, 2 striped candies, and 4 gold-wrapped

candies. If 15 students select one candy at a

time out of the bag and replace the candy

after each draw, how many students would be

expected to select a gold-wrapped candy

from the bag?

A. 4 students B. 5 students

C. 15 students D. 60 students

Respuesta :

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joaobezerra joaobezerra · Answer 1 · 2022-01-19T11:09:30+01:00

Using the binomial distribution, it is found that the number of students that would be expected to select a gold-wrapped candy from the bag is given by:

B. 5 students

The candies are chosen with replacement, which means that for each student, the probability of choosing a gold wrapped candy is independent of any other student, hence the binomial distribution is used.

What is the binomial distribution?

The binomial distribution is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this problem:

There are 15 students, hence [tex]n = 15[/tex].

Of a totlal of 5 + 1 + 2 + 4 = 12 candies, 4 are gold wrapped, hence [tex]p = \frac{4}{12} = \frac{1}{3}[/tex]

Then, the expected value is:

[tex]E(X) = np = 15\times \frac{1}{3} = 5[/tex]

Hence, option B is correct.

To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377