Compute the indicated quantity
P(A probability B) = .1, P(B) = .5. Find P(A interception B).
Missing information.
You'll need three pieces of information to find the fourth in the following relation:
P(A∪B)=P(A)+P(B)-P(A∩B)
To find the probability of the intersection (A ∩ B), which represents the event where both event A and event B occur, we can utilize the formula:
P(A ∩ B) = P(A) × P(B)
However, we need to be cautious because the probability we have been given is P(A | B), not P(A). Let's start by understanding what P(A | B) means.
P(A | B) represents the probability of event A occurring given that event B has already occurred. It can be calculated using the formula:
P(A | B) = P(A ∩ B) / P(B)
We have P(A | B) = 0.1 and P(B) = 0.5. We can rearrange the equation to find P(A ∩ B):
P(A ∩ B) = P(A | B) × P(B)
Now, we can substitute the given values:
P(A ∩ B) = 0.1 × 0.5
Simplifying this equation gives us:
P(A ∩ B) = 0.05
Therefore, the probability of the intersection (A ∩ B) is 0.05.