Question

A box contains 3 black pens, 7 blue pens, and 5 red pens. She pulls a red pen, puts it back, pulls a blue pen, puts it back, and then pulls a black pen and uses it. P(red, then blue, then black)

Answer 1

7/25

Explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome/total outcome

If the box contains 3 black pens, 7 blue pens, and 5 red pens, the total number of pens in the box is 3+7+5 = 15pens

Probability of pulling a red pen and replacing = 5/15 = 1/3

Probability of pulling a blue pen and replacing = 7/15

Probability of pulling a black pen and not replacing(using it) = 3/15

{Note that the total number of outcome used will still be 15 since the black pen was pulled out last even though it wasn't replaced.}

P(red, then blue, then black) = 1/3×7/15×3/15

= 63/225

= 7/25