# Suppose a poll of 851851adults asked how to deal with an energy​ shortage: use more​ production, more​ conservation, or both. Suppose 3 people are selected at random from this​ sample, and that the same person can be selected more than once. Complete parts a through d below.ResponseNumber   More production302302More conservation425425Both9494No opinion3030Total851851​a) What is the probability that all three responded​ "More conservationconservation​?" . 499 ​(Round to three decimal places as​ needed.) I watched every video that the professor gave and not one has an example like this.  Please show your work as there are other questions for this same problem but I do not know what they are yet.

Question

Suppose a poll of 851851

adults asked how to deal with an energy shortage: use more production, more conservation, or both. Suppose 3 people are selected at random from this sample, and that the same person can be selected more than once. Complete parts a through d below.

Response
Number
More production
302302
More conservation
425425
Both
9494
No opinion
3030
Total
851851
a) What is the probability that all three responded "More
conservationconservation?"

. 499
(Round to three decimal places as needed.)

I watched every video that the professor gave and not one has an example like this.  Please show your work as there are other questions for this same problem but I do not know what they are yet.

Step 1

Concept of probability:

Probability deals with the likelihood of occurrence of a given event. The probability value lies between 0 and 1. An event with probability 1 is considered as certain event and an event with probability 0 is considered as an impossible event. The probability of 0.5 infers of having equal odds of occurring and not occurring of an event.

The general formula to obtain probability of an event A is,

P(A) = (number of favorable elements for event A)/(Total number of elements in the sample space).

The basic properties of probability are given below:

Step 2

Find the probability of the response “more conversation”:

The total number of people in the poll is n(S) = 851.

Consider the event A be the number of people responded to more conversation.

The number of people responded more conversation is n(A) = 425.

The probability of the response “more conversation” is obtained as 0.4994 from the calculation given below:

Step 3

Find the probability that all the selected 3 people responded “more conversation”:

Here, it is given that the investigator selects 3 people.

The probability that all the selected 3 people responded “more conversation” is the product of probability that the first person respond “more conversation”, the second person respond “more conversation” and the third person respond &ldqu...

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