hi!
how would you figure out a problem where you are given a probability of success for 12 people and you are trying to find the probability of success for 1 person?
Can you assume the probability of success is the same for everybody? Does success for 12 mean that each person was successful? If so.
Let p=probablity of success for one person. Let x be the known probability of success for 12 people.
So for 12 people p^12 = x.
Take natural logs of both sides.
12*ln(p) = ln(x). So
ln(p) = ln(x)/12. Ln(x)/12 is a known number -- call it h.
so p = e^h.
QED
Take the natural logs of both sides.
Hi there! To find the probability of success for one person given the probability of success for 12 people, you will need to use a concept called "Conditional Probability".
Conditional Probability is a measure of the probability of an event occurring, given that another event has already occurred. In this case, you want to find the conditional probability of success for one person, given the probability of success for 12 people.
Here's how you can approach this problem step by step:
1. Start by finding the probability of success for all 12 people. Let's call this probability "P(12_success)".
2. Now, imagine that you know that one person out of the 12 is successful. You want to find the probability that a specific person is successful out of the 12, given this information.
3. Since you know that one person is already successful, you can treat this as a new situation where you have 11 people left, with 11 successes remaining. Let's call this probability "P(11_success)".
4. The probability of success for one person, given the success of the 11 others, can then be calculated by dividing the probability of success for 11 people by the total number of remaining people (11 in this case): P(11_success)/11.
To summarize, to find the probability of success for one person, given the probability of success for 12 people, you divide the probability of success for 11 people by 11.
I hope this explanation helps! Do let me know if you need any further clarification.