A tourist bureau survey showed that 80% of those who seek information about the state actually come to visit. The office received 7 request for information. What is the probability that all will visit?
What is the probability that at least one will?
I've tried to figure how to get the answer but I can't seem to understand how to do this one
To find the probability that all seven visitors will actually come to visit, we need to multiply the probabilities of each individual visitor coming to visit.
Given that 80% of those who seek information actually visit, the probability of one visitor actually coming to visit is 0.8. Therefore, the probability that all seven visitors will come to visit is calculated as follows:
P(all will visit) = 0.8 * 0.8 * 0.8 * 0.8 * 0.8 * 0.8 * 0.8
= (0.8)^7
= 0.2097
Thus, the probability that all seven visitors will actually come to visit is approximately 0.2097 or 20.97%.
To find the probability that at least one visitor will come to visit, we can use the complementary probability approach.
The probability that at least one visitor will come to visit is equal to 1 minus the probability that none of them will visit.
Given that 80% of those who seek information actually visit, the probability that one visitor will not visit is 1 - 0.8 = 0.2. Therefore, the probability that none of the seven visitors will come to visit is calculated as follows:
P(none will visit) = 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2
= (0.2)^7
= 0.000128
Thus, the probability that at least one of the seven visitors will actually come to visit is equal to 1 minus the probability that none will visit:
P(at least one will visit) = 1 - P(none will visit)
= 1 - 0.000128
= 0.999872
Therefore, the probability that at least one of the seven visitors will actually come to visit is approximately 0.999872 or 99.99%.