About 8% of the population of a large country is nervous around strangers. If two people are randomly selected, what is the probability both are nervous around strangers? What is the probability at least one is nervous around strangers?
0.0064
Well, well, well, let's do some probability math, shall we?
If 8% of the population is nervous around strangers, that means the probability for one person to be nervous around strangers is 8% or 0.08. Since we are selecting two people randomly, we need to multiply the probabilities.
So, the probability that both people are nervous around strangers is 0.08 * 0.08 = 0.0064, or about 0.64%.
Now, for the probability of at least one person being nervous around strangers, we need to do a bit of reverse thinking. The probability that none of them are nervous around strangers is the complement of at least one person being nervous.
The probability that none of them are nervous is 1 - probability of at least one person being nervous. So, 1 - 0.0064 = 0.9936, or about 99.36%.
So, there you have it! The probability that both people are nervous around strangers is about 0.64%, and the probability of at least one person being nervous around strangers is about 99.36%.
To find the probability of both people being nervous around strangers, we can multiply the probabilities of each event happening consecutively.
1. Probability both people are nervous around strangers:
The probability of the first person being nervous around strangers is 8% or 0.08.
After the first person is chosen, there will be one less person in the population, so the probability of the second person being nervous around strangers will be slightly different.
Since we are randomly selecting two people without replacement, the probability of the second person being nervous around strangers will now be based on the remaining population size.
Let's assume the population size is very large, so the probability will remain similar.
Therefore, the probability of both people being nervous around strangers is:
0.08 (probability of the first person) * 0.08 (probability of the second person) = 0.0064 or 0.64%
2. Probability at least one person is nervous around strangers:
To find this probability, we can use the concept of complementary events.
The complementary event of "at least one person is nervous around strangers" is "no person is nervous around strangers."
So, to find the probability at least one person is nervous around strangers, we subtract the probability of no person being nervous around strangers from 1.
The probability of no person being nervous around strangers is equal to the complement of the probability of one person being nervous around strangers.
The probability of one person being nervous around strangers is 8% or 0.08.
Therefore, the probability of no person being nervous around strangers is:
1 - 0.08 = 0.92 or 92%.
Hence, the probability of at least one person being nervous around strangers is:
1 - 0.92 = 0.08 or 8%.
0.098
Probability of 2 or more independent events occurring is found by multiplying the individual events
Assuming replacement, P(both) = .08 * .08
At least one = one or two. Either-or probabilities are found by adding the individual probabilities.
P(one) = .08 * .92
P(both) shown above