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 tourists will visit, we can use the concept of independent events. Since each request for information is independent of the others, we can multiply the probability of each event occurring.
Given that 80% of those who seek information actually visit, the probability of any single tourist visiting is 0.80, or 80%. Therefore, the probability that all seven tourists will visit is:
P(all will visit) = (0.80)^7 = 0.3277 or approximately 32.77%
To find the probability that at least one tourist will visit, we can use the concept of complementary events. The complementary event of "at least one will visit" is "none will visit."
Therefore, the probability that none of the tourists will visit is:
P(none will visit) = (1 - P(one will visit))
Since each request for information is independent, the probability that a single tourist will not visit is 1 - 0.80 = 0.20, or 20%.
Using the concept of independence, the probability that none of the seven tourists will visit is:
P(none will visit) = (0.20)^7 = 0.000128 or approximately 0.0128%
Finally, to calculate the probability that at least one tourist will visit, we subtract the probability of none of them visiting from 1:
P(at least one will visit) = 1 - P(none will visit) = 1 - 0.000128 = 0.999872 or approximately 99.99%
So, the probability that at least one tourist will visit is about 99.99%.