ANSWER AT THE BOTTOM
Question:
There is a bag with 1 red pen, 4 black pens, and 3 blue pens. If 2 pens are chosen from the bag without replacement, what is the probability that you chose 2 black pens.
Step-by-step explanation:
Right now there are a total of 8 pens. 4 of them are black. So, the probability of choosing a black pen right now is 4/8, or 1/2.
Lets assume we picked a pen and got black.
Now there are only 7 pens in the bag, and only 3 of them are black. The probability of choosing a black pen right now is 3/7.
So on the first draw, the probability is 1/2
And on the second draw, the probability is 3/7
To find the probability of 2 ocurrences happening in a row, we must multiply their individual probabilities.
For example, if we wanted to find the probability of rolling two 6's in a row on a dice, we would need to mutiply the individual probability together. The probability of rolling one 6 is 1/6, so the probability of rolling two 6's in a row is 1/6 MULTIPLIED BY 1/6, which is 1/36.
The probability of rolling two 6's in a row is 1/36.
Lets apply the same principle to our situation right now.
So on the first draw, the probability is 1/2
And on the second draw, the probability is 3/7
1/2 MULTIPLIED BY 3/7 = 3/14
3/14 in decimal form is 0.21
ANSWER:
0.21, OR 21%