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 calculate the probabilities, we need to use the information provided.
It is given that 80% of those who seek information about the state actually come to visit. So, out of 100 people who seek information, 80 of them visit.
Let's start with the first question:
"What is the probability that all will visit?"
There are 7 requests for information. We need to find the probability that all 7 people will visit.
Since each request is independent of one another, we can multiply the individual probabilities together. Each person has a 80% chance of visiting, which is equivalent to a probability of 0.8.
So, to find the probability that all will visit, we multiply 0.8 by itself 7 times:
P(all will visit) = 0.8^7
Calculating this, we get:
P(all will visit) ≈ 0.2097
Therefore, there is approximately a 20.97% chance that all 7 people will visit.
Now let's move on to the second question:
"What is the probability that at least one will?"
To calculate this probability, we can use the complement rule, which states that the probability of an event happening is 1 minus the probability of it not happening.
In this case, the probability of at least one person visiting is equal to 1 minus the probability of none of them visiting.
Since each request is independent, the probability of one person not visiting is 1 minus their probability of visiting, which is 1 - 0.8 = 0.2.
So, the probability of none of them visiting is equal to 0.2 raised to the power of 7 (since there are 7 people).
P(none will visit) = 0.2^7
Calculating this, we get:
P(none will visit) ≈ 0.000128
Now, we can find the probability of at least one person visiting by subtracting the probability of none visiting from 1:
P(at least one will visit) = 1 - P(none will visit)
P(at least one will visit) ≈ 1 - 0.000128 ≈ 0.999872
Therefore, there is approximately a 99.99% chance that at least one out of the 7 people will visit.