Question

Box A has 14 black pens and 6 blue pens box B has 9 black pens and 3 blue pens a pen is randomly chosen from each box list these events from least likely to most likely

Answer 1

Answer:

The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

Black - Black

Black - Blue

Blue - Black

Blue - Blue

Probability of each outcome:

Black-Black:

14 out of 20, and then 9 out of 12. So

$P_{BkBk} = \frac{14}{20} \times {9}{12} = \frac{14*9}{20*12} = \frac{126}{240}$

Black-Blue:

14 out of 20, then 3 out of 12. So

$P_{BkBl} = \frac{14}{20} \times {3}{12} = \frac{14*3}{20*12} = \frac{42}{240}$

Less likely than black-black.

Blue - Black:

6 out of 20, then 9 out of 12. SO

$P_{BlBk} = \frac{6}{20} \times {9}{12} = \frac{6*9}{20*12} = \frac{54}{240}$

More likely than black-blue, less likely than black-black.

Blue - Blue

6 out of 20, then 3 out of 12

$P_{BlBl} = \frac{6}{20} \times {3}{12} = \frac{6*3}{20*12} = \frac{18}{240}$

Least likely of the outcomes.

List these events from least likely to most likely:

The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black