Suppose there is a 11.2% probability that a randomly selected person is aged 20 years or older and is also a jogger. In addition there is a 23.8% chance that a person is 20 years or older, female, given that he or she also jogs. What is the probability a randomly selected person will be female, 20 or older, and also a jogger?
I'm trying to use the conditional probability but it isn't working out=(
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Assuming that you are saying that 23.8% of the 11.2% of the 20+ joggers are female, I would say .112 * .238 = ,0267.
However, the female joggers cannot be "he."
To solve this problem, let's break it down step by step.
Let's assume P(A) represents the probability of being a jogger, P(B) represents the probability of being 20 years or older, and P(C) represents the probability of being female.
Given information:
- P(A) = 11.2% (probability of being a jogger)
- P(B|A) = 23.8% (probability of being 20 years or older given that the person is a jogger)
We need to find P(C∩B∩A), which represents the probability of being female, 20 years or older, and a jogger.
Using conditional probability, we can express this as:
P(C∩B∩A) = P(C|B∩A) * P(B∩A)
Now, we need to calculate each term separately:
1. P(B∩A) represents the probability of being 20 years or older and a jogger. This can be calculated as the intersection of the probabilities of being 20 years or older and a jogger:
P(B∩A) = P(B) * P(A)
2. P(C|B∩A) represents the probability of being female given that the person is 20 years or older and a jogger. This can be calculated as the conditional probability of being female, given that the person is 20 years or older and a jogger:
P(C|B∩A) = P(C∩B∩A) / P(B∩A)
Substituting the given values into the equations, we have:
P(B∩A) = P(B) * P(A) = 0.112 * 0.238
P(C|B∩A) = P(C∩B∩A) / P(B∩A) = P(C∩B∩A) / (0.112 * 0.238)
Finally, we can find P(C∩B∩A) by multiplying P(B∩A) and P(C|B∩A):
P(C∩B∩A) = P(B∩A) * P(C|B∩A) = (0.112 * 0.238) * [P(C∩B∩A) / (0.112 * 0.238)]
We can now solve this equation and calculate the probability.
To find the probability that a randomly selected person is female, 20 years or older, and also a jogger, we can use the concept of conditional probability.
Let's denote the events as follows:
A = Person is aged 20 years or older
B = Person is a jogger
C = Person is female
We are given the following probabilities:
P(A and B) = 0.112 (probability that a randomly selected person is aged 20 years or older and a jogger)
P(A|B) = 0.238 (probability that a person is 20 years or older, given that they also jog)
We are asked to find P(C and A and B), which represents the probability that a person is female, 20 years or older, and a jogger.
Using the formula for conditional probability, we can express P(C and A and B) as:
P(C and A and B) = P(C | A and B) * P(A and B)
Now, since we don't have the information to directly calculate P(C | A and B), we can use the rule of conditional probability:
P(A and B and C) = P(A and B) * P(C | A and B)
P(C | A and B) = P(A and B and C) / P(A and B)
Substituting the values we have, we get:
P(C and A and B) = P(A and B) * P(C | A and B) = P(A and B) * (P(A and B and C) / P(A and B))
Now, substituting the given probabilities:
P(C and A and B) = 0.112 * (P(A and B and C) / 0.112) = P(A and B and C)
Therefore, the probability that a randomly selected person will be female, 20 or older, and also a jogger is equal to the probability of the intersection of events A, B, and C, which is simply 0.112 or 11.2%.