If you're seeing this message, it means we're having trouble loading external resources on our website.

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

### Course: Grade 8 (VA SOL)>Unit 8

Lesson 7: Independent & dependent events

# General multiplication rule example: dependent events

We can use the general multiplication rule to find the probability that two events both occur when the events are not independent. Created by Sal Khan.

## Want to join the conversation?

• I have another question. What is the possibility that Doug doesn't draw silk?
• The key to this question is finding the probability that Doug draws silk.

In order for Doug to get silk, Maya first has to not get silk (5/6 chance) then Doug has to draw silk (1/5 chance).

So this means that Doug has a (5/6)*(1/5) or 1/6 chance of drawing silk. If he has a 1/6 chance of drawing silk, then that means that he has a 5/6 chance of not drawing silk.
• What is the difference between mutually exclusive event and the independent event?
(1 vote)
• Two events are independent if the occurrence of either event doesn't affect the probability of the other. Coin tosses are independent because a coin has no memory of previous flips; each toss has 50% chance of heads, no matter the previous results.

Two events are mutually exclusive if only one of them can occur. If I toss a coin, the events 'heads' and 'tails' are mutually exclusive, because they cannot both occur on the same toss.
• How do we know when to use the ind or dep of the general multiplication rule formula in a problem? How do we distinguish?
(1 vote)
• Independent events are two events in which the outcomes do not affect each other. Examples include flipping a coin.

Dependent events are two events in which the first event that occurred affects the outcome of the second event. Examples include drawing names out of a hat, without replacement.

In independent events, you use the multiplication rule with the same probability for the second event as when you started. For example, with flipping a coin, the probability of getting heads is 1/2, and the probability of getting tails is the same as that. So, the probability of flipping heads and then tails is 1/2 x 1/2, or 1/4.

For dependent events, you modify the probability of the second event to accommodate what happened in the first one. For example, if there are 10 different names in the hat and you draw one name (probability of 1/10), and don't replace it, there are nine names left in the hat. Now the probability of getting another name is 1/9. So, the probability of getting those certain names is 1/10 x 1/9, or 1/90.

Hope this helps!!