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A student has a 30% chance of receiving chocolate ice cream for dessert at lunch. A statistics class designs a simulation to approximate the probability of 5 students receiving chocolate ice cream for dessert. For the simulation, the classmates create a spinner divided into 10 equal-sized sections and label each section either “Chocolate Ice Cream” or “Not Chocolate Ice Cream” to represent the type of dessert a student receives.

How many sections of the spinner should the class label “Chocolate Ice Cream”?

3
4
6
7 hurry pls

Sagot :

meamajewski

Answer:

3

Step-by-step explanation:

30 % as a fraction is 30/100

since the are doing 10 sections we must simplify 100 to 10 so

[tex]\frac{30}{100} =\frac{3}{10}[/tex]

so this means 3 out of 10 of the sections would be labeled chocolate icecream

The count of the sections the class should label as "Chocolate Ice Cream" is 3.

How to calculate the probability of an event?

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For the considered case, it is given that:

Probability of an student getting Chocolate Ice Cream for dessert at lunch =  30% = 0.3

The count of the sections the class should label as "Chocolate Ice Cream" should be such that spinner getting "Chocolate Ice Cream" as option should have the probability as 0.3

Let the count of the sections the class should label as "Chocolate Ice Cream"  be [tex]x[/tex]

Then, as there are in total 10 sections in the spinner, and all sections are assumingly equally probable, thus, if the event E is:

E = event of getting "Chocolate Ice Cream" in the spinner ,

then as n(E) = [tex]x[/tex] (as there are [tex]x[/tex] sections with label "Chocolate Ice Cream")

and n(S) = total count of sections (size of sample space)  = 10

Thus, we get probability of event E as:

[tex]P(E) = \dfrac{n(E)}{n(S)} = \dfrac{x}{10}[/tex]

This needs to be equal to 0.3, thus,

[tex]0.3 = \dfrac{x}{10}\\x = 3[/tex]


Thus, the count of the sections the class should label as "Chocolate Ice Cream" is 3.

Learn more about probability here:

brainly.com/question/1210781

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