1. If P(A) = 0.4 P(B) = 0.2 and P(A or B) = 0.5, find the sum of P(A and B) and P(A|B).
-How would I even start this question?
2. Let A and B be two mutually exclusive events for which P(A) = 0.15 and P(B) = 0.3. Find P(A and B).
-If it's mutually exclusive, wouldn't that just go for the P(A or B)? How would you find P(A and B)?
P(A and B) = P(A) + P(B) - P(A or B)
=.4 + .2 - .5
= .1
P(A|B) is a conditional probability
Of the top of my head I am not really sure of the formula. I would have to Google it, but it is easy to find
2. Mutually exclusive means that the result of one event has not effect on another.
e.g. suppose you flip a coin and toss a die
what is the prob that you would get Heads and a 5
prob(heads AND a 5) = (1/2)(1/6) = 1/12
but ..
what is the prob that would get heads OR a 5
= 1/2 + 1/6 = 2/3
so for your problem,
P(A and B) = .15(.3) = .045
P(A or B) = .15 + .3 = .45
Thank You
To answer both questions, we'll use some basic probability concepts and formulas. Let's tackle them one by one.
1. To find the sum of P(A and B) and P(A|B), we can use the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B).
We are given:
P(A) = 0.4
P(B) = 0.2
P(A or B) = 0.5
First, let's find P(A and B):
Using the formula, we have:
P(A or B) = P(A) + P(B) - P(A and B)
0.5 = 0.4 + 0.2 - P(A and B)
0.5 = 0.6 - P(A and B)
P(A and B) = 0.6 - 0.5
P(A and B) = 0.1
Now, let's find P(A|B):
P(A|B) represents the probability of event A happening given that event B has already occurred. In this case, we have no information about the relationship between A and B, so we cannot determine P(A|B) solely from the given probabilities.
2. For mutually exclusive events, the events cannot happen at the same time. Therefore, P(A and B) in this case would be 0.
Mutually exclusive events have no overlap, so the probability of both events occurring together is always 0. In other words:
P(A and B) = 0 for mutually exclusive events.
To find P(A or B) for mutually exclusive events, you can use the formula:
P(A or B) = P(A) + P(B) since there is no overlap between A and B.
Given:
P(A) = 0.15
P(B) = 0.3
Using the formula, we have:
P(A or B) = P(A) + P(B)
P(A or B) = 0.15 + 0.3
P(A or B) = 0.45
So, in this case, P(A and B) = 0 and P(A or B) = 0.45.