The Big Idea: Dependent events
In probability dependent events are when what happens in the first event affects what happens in the second event.
For example:
A jar contains 36 marbles. There are 10 green marbles, 12 blue marbles, and 14 red marbles. Find the probability that you pick a green marble, keep it, and then pick another green marble.
The probability of picking the first green marble is $\tfrac{10}{36}$, since there are $10$ green marbles and 36 marbles in the jar.
$P(green) = \tfrac{10}{36}$
The probability of picking the second green marble is $\tfrac{9}{35}$, since we did not replace the first green marble there are only 9 green marbles left in the jar and 35 marbles left in the jar.
$P(second$ $green) = \tfrac{9}{35}$
The probability of picking a green and then a second green marble is:
$P(two$ $green$ $marbles) = \tfrac{10}{36} * \tfrac{9}{35} = \tfrac{90}{1260}$ which reduces to $\tfrac{1}{14}$
So there is a $\tfrac{1}{14}$ chance of picking two green marbles in this situation.
