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Bag contains one red pen, four black pens, and three blue pens. Two pens are randomly chosen from the bag and

are not replaced.
To the nearest hundredth, what is the probability that a black pen IS chosen first and then another black pen is
chosen?

User PanDe
by
3.1k points

1 Answer

17 votes
17 votes

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%

User Alexey Nazarov
by
3.1k points