Solution

.5+.4-.1

The solution is .8.

Now, let’s define conditional probability. The conditional probability is the chance that something occurs given something else has happened. We say for example, if we know event B has happened, what’s the chance that event A happens? What it will boil down to is finding how likely the two events are to occur together and dividing it by how likely the B event is to occur in general.

Find P(A|B) and P(B|A) in the last example….

.1/.4
.1/.5

As you can see these two do not have to equal one and other.

P(A|B) and P(B|A) for mutually exclusive events will always be 0 because there is no chance that the two events occur at the same time.

Now, what if an event has no effect on another event, then we call the events independent meaning the chances it happens when B occurs is the same as if we don’t know if B occurs.

If two events are independent, then the chances they happen at the same time equals the two probabilities multiplied.

If we had a table like so, what are the chances that either A or B happen? Find the probabilities, don’t just count.

pB = (20+40)/100
pA = (20+30)/100
pAB = 20/100
print(pA+pB-pAB)

The probability is .9!

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