A sc tourists bureau survey showed that 75 % of those who seek information about the state actually come to visit . The office received 8 requests for information. What is the probability that probability that 4 to 6 inclusive of the people will visit sc?

To calculate the probability, we need to use the binomial probability formula. The formula is given as follows:

P(x) = (nCx) * (p^x) * (q^(n-x))

Where:
P(x) is the probability of getting exactly x successes
n is the total number of trials or requests (8 in this case)
x is the number of successful outcomes (between 4 and 6, inclusive)
p is the probability of success (75% or 0.75 in this case)
q is the probability of failure (100% - p or 25% or 0.25 in this case)
nCx is the number of ways to choose x items from n items, and it is calculated as n! / (x! * (n-x)!)

Using this formula, we can calculate the probabilities for 4, 5, and 6 successful outcomes and sum them up to get the final probability.

P(4 to 6 inclusive) = P(4) + P(5) + P(6)

P(4) = (8C4) * (0.75^4) * (0.25^(8-4))
P(5) = (8C5) * (0.75^5) * (0.25^(8-5))
P(6) = (8C6) * (0.75^6) * (0.25^(8-6))

To calculate these values, we need to find the combinations:

8C4 = 8! / (4! * (8-4)!) = 70
8C5 = 8! / (5! * (8-5)!) = 56
8C6 = 8! / (6! * (8-6)!) = 28

Now we can plug in these values to calculate the probabilities:

P(4) = 70 * (0.75^4) * (0.25^(8-4))
P(5) = 56 * (0.75^5) * (0.25^(8-5))
P(6) = 28 * (0.75^6) * (0.25^(8-6))

Finally, we add these probabilities to get the overall probability:

P(4 to 6 inclusive) = P(4) + P(5) + P(6)