a bag contains one red pen, four black pens, and three blue pens. two pens are randomly chosen from the bag…

a 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? 0.02 0.19 0.21 0.25

a 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? 0.02 0.19 0.21 0.25

Answer

Explanation:

Step1: Calculate total number of pens

There is 1 red + 4 black + 3 blue = 8 pens initially.

Step2: Calculate probability of first - black pen

The probability of choosing a black pen first is $\frac{4}{8}$ since there are 4 black pens out of 8 total pens.

Step3: Calculate probability of second - black pen

After choosing a black pen first (without replacement), there are 3 black pens left and 7 pens in total. So the probability of choosing a black pen second is $\frac{3}{7}$.

Step4: Calculate combined probability

The probability of both events happening is the product of the probabilities of each event. So $P=\frac{4}{8}\times\frac{3}{7}=\frac{12}{56}\approx0.21$.

Answer:

0.21