8. Independent and Dependent Events
If the occurrence or non-occurrence of E1 does not affect the probability of occurrence of E2, then
P(E2 | E1) = P(E2)
and E1 and E2 are said to be independent events.
Otherwise they are said to be dependent events.
[Recall from Conditional Probability that the notation P(E2 | E1) means "the probability of the event E2 given that E1 has already occurred".]
Let's consider "E1 and E2" as the event that "both E1 and E2 occur".
If E1 and E2 are dependent events, then:
P(E1 and E2) = P(E1) × P(E2 | E1)
If E1 and E2 are independent events, then:
P(E1 and E2) = P(E1) × P(E2)
For three dependent events E1, E2, E3, we have
P(E1 and E2 and E3) = P(E1) × P(E2 | E1) × P(E3 | E1 and E2)
For three independent events E1, E2, E3, we have
P(E1 and E2 and E3) = P(E1) × P(E2) × P(E3)
If the probability that person A will be alive in `20` years is `0.7` and the probability that person B will be alive in `20` years is `0.5`, what is the probability that they will both be alive in `20` years?
A fair die is tossed twice. Find the probability of getting a `4` or `5` on the first toss and a `1`, `2`, or `3` in the second toss.
Two balls are drawn successively without replacement from a box which contains `4` white balls and `3` red balls. Find the probability that
(a) the first ball drawn is white and the second is red;
(b) both balls are red.
A bag contains `5` white marbles, `3` black marbles and `2` green marbles. In each draw, a marble is drawn from the bag and not replaced. In three draws, find the probability of obtaining white, black and green in that order.
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Math Lessons on DVD
Easy to understand math lessons on DVD. See samples before you commit.
More info: Math videos
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!