A and B are events defined on a sample space, with the following probabilities. Find P(A and B). (Give your answer correct to two decimal places.)
P(A) = 0.5 and P(B | A) = 0.4
By definition:
P(B|A)=P(B∩A)/P(A)
So
0.4=P(B∩A)/0.5
Solve for P(B∩A)
Well, it seems like A and B are not getting along so well.
Since P(B | A) = 0.4, this means that the probability of event B happening given that event A has already occurred is 0.4.
Now, to find P(A and B), we can use the formula:
P(A and B) = P(A) * P(B | A)
Plugging in the values:
P(A and B) = 0.5 * 0.4
And the answer is 0.20.
So, the probability of both A and B happening is 0.20 or 20%. I hope A and B can resolve their differences!
To find P(A and B), we need to use the formula for conditional probability.
P(A and B) = P(A) * P(B | A)
Given that P(A) = 0.5 and P(B | A) = 0.4, we can substitute these values into the formula:
P(A and B) = 0.5 * 0.4
Multiplying these values, we get:
P(A and B) = 0.2
Therefore, the probability of events A and B occurring together is 0.2 or 20%.
To find the probability of A and B occurring together, denoted as P(A and B), we need to use the formula for conditional probability:
P(A and B) = P(A) * P(B | A)
Given that P(A) = 0.5 and P(B | A) = 0.4, we can substitute these values into the formula:
P(A and B) = 0.5 * 0.4
Multiplying these values together, we find:
P(A and B) = 0.2
Therefore, the probability of events A and B occurring together is 0.2, or 20% when expressed as a percentage.