A poll is given, showing 20% are in favor of a new building project.
If 5 people are chosen at random, what is the probability that greater than 4 of them favor the new building project?
Wouldn't greater than 4 in 5 choosings just be all 5 ??
so what is (1/5)^5 ?
Donovan, are you sure you do not have a typo? Greater than 4 is just all five of them.
To determine the probability that greater than 4 people out of 5 favor the new building project, we need to calculate the probability of each possible outcome and then sum up the probabilities of the desired outcomes.
First, let's consider the number of people who favor the new building project:
- If none of the 5 people favor the project, then the probability is (0.8)^5, as each person has an 80% chance of not favoring it.
- If exactly 1 person favors the project, then the probability is 5C1 * (0.8)^4 * (0.2)^1, where 5C1 represents choosing 1 person out of 5.
- If exactly 2 people favor the project, then the probability is 5C2 * (0.8)^3 * (0.2)^2.
- If exactly 3 people favor the project, then the probability is 5C3 * (0.8)^2 * (0.2)^3.
- If exactly 4 people favor the project, then the probability is 5C4 * (0.8)^1 * (0.2)^4.
Lastly, we want to find the probability of greater than 4 people favoring the project, which means we need to calculate the probability of exactly 5 people favoring the project. This probability is 5C5 * (0.8)^0 * (0.2)^5.
To get the total probability, we sum up the probabilities for each case:
P(greater than 4 people favor the project) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5).
Now, we can calculate the probabilities:
P(0) = (0.8)^5
P(1) = 5C1 * (0.8)^4 * (0.2)^1
P(2) = 5C2 * (0.8)^3 * (0.2)^2
P(3) = 5C3 * (0.8)^2 * (0.2)^3
P(4) = 5C4 * (0.8)^1 * (0.2)^4
P(5) = 5C5 * (0.8)^0 * (0.2)^5
Finally, sum up the probabilities, excluding P(0) through P(4), to get the probability of greater than 4 people favoring the project:
P(greater than 4 people favor the project) = P(5)
Solving these calculations will give you the probability you are looking for.