<u><em>ANSWER AT THE BOTTOM</em></u>
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<u><em>Question:</em></u>
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.
<u><em>Explanation:</em></u>
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.
<u><em>So on the first draw, the probability is 1/2</em></u>
<u><em>And on the second draw, the probability is 3/7</em></u>
<em>To find the probability of 2 ocurrences happening in a row, we must multiply their individual probabilities.</em>
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.
<u><em>So on the first draw, the probability is 1/2</em></u>
<u><em>And on the second draw, the probability is 3/7</em></u>
1/2 MULTIPLIED BY 3/7 = 3/14
3/14 in decimal form is <u><em>0.21</em></u>
<u><em>ANSWER:</em></u>
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0.21, OR 21%