Question

1. a bag contains 10 red pens, 15 blue pens, and 20 black pens. joseph will pull a pen from the bag. which equation describes the probability of joseph selecting a black pen? \\( \mathrm{p(black\\ pen)} = \frac{15}{45} \\) \\( \mathrm{p(black\\ pen)} = \frac{20}{45} \\) \\( \mathrm{p(black\\ pen)} = \frac{45}{20} \\) \\( \mathrm{p(black\\ pen)} = \frac{10}{45} \\)

Explanation:

Step1: Calculate total number of pens

Add the number of red, blue, and black pens: \(10 + 15 + 20 = 45\) total pens.

Step2: Determine probability formula

Probability of an event is \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). For black pens, favorable outcomes = 20, total outcomes = 45. So \(P(\text{black pen})=\frac{20}{45}\).

Answer:

\( \text{P(black pen)} = \frac{20}{45} \) (the second option)