consider a jar of 45 marbles: 18 blue, 12 red, 9 green, and 6 white.
find the probability of pulling out a blue marble,not replacing it, then pulling out another blue marble.
In probability we have two types of events:
Independent: Events who's probability is not affected by the previous event(s).
Dependent: Events who's probability can be affected by preious event(s).
What we have in this case is a dependent event because when we don't replace the marble, it changes the amount of total marbles inside the jar and thus the chances of drawing another marble changes.
Because one event relys on the other we must find their probabilities separately at first. So what we do is figure out the probability of pulling out a blue marble and then the probability of pulling out another after not replacing the first. We will call these event 1 and 2.
Event 1: To find the probability of pulling out a blue marble we just divide the amount of blue marbles we have by the total marbles in the jar:
18/45. We will keep it in this form because this is the standard way of representing chances in stats classes.
Event 2: Now what we have left are 17 blue marbles and a total of 44 marbles so the chances of drawing a blue marble now become:
To combine these two chances we now multiply them together:
18/45*17/44. We will of course have to find a least common denominator but that's not hard and I'm sure you could do that part on your own.
Hope this helped!
The probability of pulling out a blue marble will be the number of blue marbles (18) divided by the total (45).
The probability of pulling out another blue marble will be the number of remaining blue marbles (17) divided by the total remaining marbles (44).
You multiply the two together like so:
18/45 x 17/44 = ?
Which gives you the probability of pulling one blue and then another.