A random sample of 15 people is taken from a population in which 40% favour a particular political stand. What is the probability that exactly 6 individuals in the sample favour this political stand?

0.4000
0.5000
0.4000
0.2066
0.0041

0.2066

0.2066

.400

Well, probability can be a bit tricky sometimes. But let's give it a shot, shall we?

To calculate the probability, we can use the binomial distribution formula. The formula looks like this:

P(X = x) = (nCx) * p^x * (1-p)^(n-x)

Where:
- n is the sample size (which is 15 in this case)
- x is the number of individuals who favor the political stand (which is 6 in this case)
- p is the probability of favoring the political stand (which is 0.4 in this case)
- (nCx) is the binomial coefficient, which can be calculated as n! / (x! * (n-x)!)

Now, let me calculate it for you. *pushes imaginary buttons on a calculator*

P(X = 6) = (15C6) * (0.4^6) * (1-0.4)^(15-6)

Okay, after the calculations, the probability that exactly 6 individuals in the sample favor the political stand is approximately 0.2066. So the answer you're looking for is 0.2066.

I hope this helps! And remember, probability is a funny thing. Sometimes it's just a roll of the dice!

To find the probability that exactly 6 individuals in a sample of 15 people favor a particular political stand, we can use the binomial probability formula.

The binomial probability formula is given by P(X=k) = nCr * p^k * (1-p)^(n-k), where:
- P(X=k) represents the probability of getting exactly k successes in a fixed number of trials.
- nCr represents the number of ways to choose k successes from n trials.
- p represents the probability of success in a single trial.
- (1-p) represents the probability of failure in a single trial.
- k is the number of successes we are interested in, which in this case is 6.
- n is the total number of trials or sample size, which in this case is 15.
- p is the probability of favoring the political stand, which is given as 40% or 0.40 in decimal form.

Let's calculate the probability using the formula:

P(X=6) = 15C6 * (0.40)^6 * (1-0.40)^(15-6)

To calculate 15C6, we need to use the combination formula: nCr = n! / (r!(n-r)!), where n! represents the factorial of n.

15C6 = 15! / (6!(15-6)!)
= (15 * 14 * 13 * 12 * 11 * 10) / (6 * 5 * 4 * 3 * 2 * 1)
= 5005

Now, substitute the values into the formula:

P(X=6) = 5005 * (0.40)^6 * (1-0.40)^(15-6)
= 5005 * (0.40)^6 * (0.60)^9
= 0.2066

So, the probability that exactly 6 individuals in the sample favor the political stand is approximately 0.2066. Therefore, the correct answer is 0.2066.

0.4000