What is probability explain conditional probability?

Answer 1

Probability is the chance of an event occurring. For example when flipping a coin you have a 50% chance that it will land on heads and a 50% chance that it will land on tails since there are only two possibilities.

Conditional probability refers to when one event is dependent on another event occurring. It can also be written as the probability of an event B occurring after event A has already occurred. The notation for conditional probability is P(B|A). (Note: this does not mean B divided by A but probability of B after A)

When two events are dependent, the probability of them both occurring is:

P(A and B)=P(A)P(B|A)

So for example: 53% of residents have home owners insurance. Of them, 27% has auto-insurance. If a resident is selected at random, what is the probability they with have both insurances?

Let H stand for home owners insurance = 53% or 0.53

Let A stand for auto insurance = 27% or 0.27

P(H and P)=P(H)P(A/H)

=(0.53)(0.27)

= 0.1431

So the probability of residents have both home owners and auto insurance is 0.1431 or 14.31%