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?
To find the probability that all 7 visitors will actually come to visit, we can use the given information that 80% of those who seek information actually visit.
1. Calculate the probability that an individual visitor will come to visit:
The probability that an individual visitor will come to visit is 80%, or 0.8.
2. Calculate the probability of all 7 visitors coming to visit:
Since all 7 visitors are independent events, and we want to find the probability of all 7 coming to visit, we multiply the individual probabilities together:
Probability(all 7 will visit) = 0.8^7 ≈ 0.2097 (or 20.97%).
Therefore, the probability that all 7 visitors will come to visit is approximately 0.2097 or 20.97%.
To find the probability that at least one visitor will come to visit:
1. Calculate the probability that an individual visitor will not come to visit:
Since the probability of an individual visitor coming to visit is 80%, or 0.8, the probability that they will not come to visit is 1 - 0.8 = 0.2.
2. Calculate the probability of none of the 7 visitors coming to visit ("no-show" probability):
Since the probability of each visitor not coming to visit is 0.2, and assuming they are independent, we multiply the individual probabilities together:
Probability(no visitor will come) = 0.2^7 ≈ 0.000128 (or 0.0128%).
3. Calculate the probability that at least one visitor will come to visit:
Since we want to find the probability of at least one visitor coming to visit, we can subtract the probability that none will come from 1 (since the sum of all probabilities equals 1):
Probability(at least one visitor will come) = 1 - Probability(no visitor will come) ≈ 0.999872 (or 99.9872%).
Therefore, the probability that at least one visitor will come to visit is approximately 0.999872 or 99.9872%.