There is a woman that has a 40% chance of being in Casper recently, a 30% chance of being in Denver and a 27% chance that she has been to both. Find the probablility that she has been to Casper if she has been to Denver.
To find the probability that the woman has been to Casper if she has been to Denver, we can use conditional probability.
The conditional probability of an event A given event B, denoted as P(A|B), is defined as the probability of event A occurring, given that event B has already occurred. In this case, event A represents the woman being in Casper, and event B represents the woman being in Denver.
We are given the following information:
- P(Casper) = 0.4 (40% chance of the woman being in Casper)
- P(Denver) = 0.3 (30% chance of the woman being in Denver)
- P(Casper ∩ Denver) = 0.27 (27% chance that the woman has been to both Casper and Denver)
To find P(Casper|Denver), we can use the formula for conditional probability:
P(Casper|Denver) = P(Casper ∩ Denver) / P(Denver)
Substituting the known values:
P(Casper|Denver) = 0.27 / 0.3
Dividing 0.27 by 0.3, we get the answer:
P(Casper|Denver) ≈ 0.9
Therefore, the probability that the woman has been to Casper if she has been to Denver is approximately 0.9 or 90%.