A brand has 50% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 6 randomly selected customers, what is the probability that exactly 5 of the selected consumers recognize the brand name?

I need the correct formula in like p = m=
in other words a language I can understand because I do not get this, please and thank you

To calculate the probability that exactly 5 out of 6 randomly selected customers recognize the brand name, you can use the binomial distribution formula.

The binomial distribution formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where:
P(X = k) is the probability of exactly k successes
n is the total number of trials (in this case, the total number of customers)
k is the number of successes (in this case, 5)
p is the probability of success (in this case, the recognition rate, which is 50% or 0.5)
(1 - p) is the probability of failure

For this problem, the values you need are:
n = 6 (since you are selecting 6 customers)
k = 5 (since you want exactly 5 customers to recognize the brand)
p = 0.5 (since the recognition rate is 50%)

Now let's plug these values into the formula:

P(X = 5) = (6 choose 5) * (0.5)^5 * (1 - 0.5)^(6 - 5)

To calculate (6 choose 5), you can use the formula for combinations:

(6 choose 5) = 6! / (5! * (6-5)!)

Simplifying this expression, you get:

6! / (5! * 1!) = 6

Now, let's substitute this value into the binomial distribution formula:

P(X = 5) = 6 * (0.5)^5 * (1 - 0.5)^(6 - 5)

Simplifying further:

P(X = 5) = 6 * (0.5)^5 * 0.5^1

Calculating the values:

P(X = 5) = 6 * 0.03125 * 0.5

P(X = 5) = 0.09375

Therefore, the probability that exactly 5 out of 6 randomly selected customers recognize the brand name is 0.09375 or 9.375%.