If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Independent and dependent events

### Basic probability

Probability is simply how likely something is to happen.

Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes (how likely they are).  The analysis of events governed by probability is called statistics.

View all of Khan Academy’s lessons and practice exercises on Probability and Statistics

The best example for understanding probability is flipping a coin:

There are two possible outcomes:  Heads or Tails

What’s the probability of the coin landing on Heads? P(H) = ?You might intuitively know that the likelihood is half/half, or 50%.  But how do we work that out?  Probability =

In this case:

Probability of an event = (# of ways it can happen) / (total number of outcomes)

P(A) = (# of ways A can happen) / (Total number of outcomes)

Practice some questions on Probability now (example question below):

Another example: rolling dice

There are six different outcomes:

What’s the probability of rolling a ‘1’?

What’s the probability of rolling a ‘1’ or a ‘6’?

Using the formula from above:

What’s the probability of rolling an even number? (i.e. rolling a 2, 4 or 6)

Tips

• The probability of an event can only be between 0 and 1 (and can also be written as a percentage)
• The probability of event A is often written as P(A)
• If P(A) > P(B) then event A has a higher chance of occurring than event B
• If P(A) = P(B) then events A and B are equally likely to occur

Next step:

Practice basic probability skills on Khan Academy - try our stack of practice questions with useful hints and answers!

Or

Watch Sal explain the basics of probability:

Or watch Sal go through an example: picking marbles from a bag

View all of Khan Academy’s lessons and practice exercises on Probability and Statistics here