what is the probability that she will pick a pen that is not black?

Question

Erica has 5 blue pens, 3 black pens, and 6 red pens in her desk drawer. If she randomly picks a pen from her drawer, what is the probability that she will pick a pen that is not black? *

Answer 1

We can think about this in terms of the probability that the pen is or isn't black. Note that:

P(pen=black) + P(pen≠black) = 1

This implies that (subtracting P(pen=black)) from both sides:

P(pen≠black) = 1 - P(pen=black)

Since 3 out of the 14 total pens are black, P(pen=black) = 3 / 14. Therefore,

P(pen≠black) = 1 - P(pen=black) = 1 - 3 / 14 = 11 / 14

This answer is equivalent as well:

P(pen≠black) = P(pen=blue) + P(pen=red) = 5 / 14 + 6 / 14 = 11 /14.

When working with probabilities, it is really helpful to think about the "complement" of a random event (such as "drawing a pen that isn't black). If we define a random event by A and its complement as A^c, we will always have:

A + A^c = 1.

Answer 2

The probability that she would pick a pen that is not black is 1 - the probability that she will pick a pen that is black.

There are 14 total pens and 3 are black, so there is a 3/14 probability she will pick a black pen and thus an 11/14 probability she will not pick a black pen.

Answer 3

Bl = blue pens

Bk = black pens

R = red pens

P(Bk^c) = 1 - P(Bk) = 1 - (3/14) = 11/14 = 0.79

The probability of selecting a pen that is not black is 0.79.