Question

Based on a​ survey, when 1009 consumers were asked if they are comfortable with drones delivering their​ purchases, 42% said yes. The probability of randomly selecting 30 of the 1009 consumers and getting exactly 24 who are comfortable with the drones is represented as 0plus. What does 0plus ​indicate? Does 0plus indicate that it is impossible to get exactly 24 consumers who are comfortable with​ drones?Choose the correct answer below.

A.The probability 0+ indicates that the probability is a very small positive value. It indicates that the event is impossible.
B.The probability 0+ indicates that the probability is a very small positive value. It indicates that the event is​ possible, but very unlikely.
C.The probability 0+ indicates that the probability is a very small positive value. It indicates that the event is likely.
D.The probability 0+ indicates that the probability is zero. It indicates that the event is impossible.

Answer 1

B.The probability 0+ indicates that the probability is a very small positive value. It indicates that the event is​ possible, but very unlikely.

Explanation:

Out of 1009 consumers a sample of 30 consumers is selected and asked the questions. So, the sample size is 30.

n = 30

Based on previous survey, 42% are comfortable with the drone. So in this sample, we can consider the probability of success to be 42%.

p = 42% = 0.42

q = 1 - p = 1 - 0.42 = 0.58

We want to find the probability of getting exactly 24 consumers who are comfortable with drones.

x = 24

Since, the sample size is fixed, the selections are independent and probability of success is constant, we can use the Binomial Probability to answer this problem. All the conditions of a Binomial Distribution are being satisfied.

According to the formula of Binomial Distribution, the probability of getting exactly x success among n trials is given as:

`P( X = x )=^(n)C_(x)(p)^(x)(q)^(n-x)`

Using the values, we get:

`P(X = 24) =^(30)C_(24)(0.42)^(24)(0.58)^(6)= 0.00002`

Thus, the probability of getting exactly 24 consumers from a sample of 30 who are comfortable with drones is 0.00002, which is extremely small.

Since, the value of probability is a very small positive number, it indicates that event is possible but very unlikely. An impossible event has probability equal to 0.

Therefore, option B gives the correct answer.