Survey on concern for criminal in a survey 3 of 4 students said the court show too much concern for criminals find the probability that 3 out of 7 randomly selected students will agree with this statement
To find the probability that 3 out of 7 randomly selected students will agree with the statement, we can use the concept of binomial probability.
Let's break down the problem:
- We have a survey with 4 options: Agree, Disagree, Not Sure, No Response.
- For the given survey, 3 out of 4 students said the court shows too much concern for criminals.
Now, let's assume that the probability of a student agreeing with the statement is the same for all students. Let's call this probability "p."
To calculate the probability, we can use the binomial probability formula:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of getting exactly k successes (students agreeing with the statement)
- n is the total number of trials (number of students randomly selected)
- k is the number of successes (number of students agreeing with the statement)
- p is the probability of success (probability of a student agreeing with the statement)
- (n C k) represents the number of combinations of n items taken k at a time (n choose k)
In this case, n = 7 (total number of students randomly selected) and k = 3 (number of students agreeing with the statement).
Now, we need to determine the value of p. Since we are given that 3 out of 4 students agree with the statement, we can calculate p as follows:
p = (number of students agreeing with the statement) / (total number of students) = 3/4 = 0.75
Now, let's plug in these values into the formula to calculate the probability:
P(X = 3) = (7 C 3) * (0.75^3) * (1 - 0.75)^(7 - 3)
Using the combination formula:
(7 C 3) = 7! / (3! * (7-3)!) = 35
Substituting the values:
P(X = 3) = 35 * 0.75^3 * 0.25^4
Calculating this expression will give you the probability that exactly 3 out of the 7 randomly selected students will agree with the statement.