A 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 find the probability that 4 to 6 inclusive people will visit South Carolina (SC) out of the 8 requests received, we need to calculate the probability of each individual scenario (4, 5, and 6 people visiting) and then sum them up.
First, let's calculate the probability when exactly 4 people visit SC:
P(4 people visiting SC) = (Probability of 4 people visiting) * (Probability of 4 people not visiting)
= (0.75)^4 * (0.25)^4
Next, let's calculate the probability when exactly 5 people visit SC:
P(5 people visiting SC) = (Probability of 5 people visiting) * (Probability of 3 people not visiting)
= (0.75)^5 * (0.25)^3
Finally, let's calculate the probability when exactly 6 people visit SC:
P(6 people visiting SC) = (Probability of 6 people visiting) * (Probability of 2 people not visiting)
= (0.75)^6 * (0.25)^2
Now, we can sum up the probabilities for each scenario to find the total probability that 4 to 6 people will visit SC:
P(4 to 6 people visiting SC) = P(4 people visiting SC) + P(5 people visiting SC) + P(6 people visiting SC)
Calculate each individual probability and add them up to find the final answer.