Problem 56 - College Algebra

Question

Write a probability word problem whose answer is one of the following fractions: \(\frac{1}{6}\) or \(\frac{1}{4}\) or \(\frac{1}{3}\)

Step-by-Step Solution

Answer

Three different probability problems were created with the respective solutions of \(\frac{1}{6}\), \(\frac{1}{4}\), and \(\frac{1}{3}\). Though these problems were formulated independently, they could be combined into a single complex problem if desired.

Step 1: Formulate a probability problem with the answer \(\frac{1}{6}\)

Imagine you have a six-sided die (standard die). The die is fair, which means all sides are equally likely to come up when rolled. When rolled, what is the probability that the number 1 appears?

Step 2: Calculation for problem in Step 1

Since there is only one face with the number 1, and there are six faces in total, the probability is therefore \(\frac{1}{6}\), which is the desired outcome.

Step 3: Formulate a probability problem with the answer \(\frac{1}{4}\)

Let's take the case where you have a bag containing 4 marbles: 1 blue, 1 green, 1 red, and 1 yellow. If you draw one marble randomly from the bag, what would be the probability that the marble drawn is blue?

Step 4: Calculation for problem in Step 3

Since there is only one blue marble, and there are four marbles in total, the probability is therefore \(\frac{1}{4}\), which is the desired outcome.

Step 5: Formulate a probability problem with the answer \(\frac{1}{3}\)

Imagine you have a box containing 3 balls: 1 white, 1 black, and 1 silver. If you choose one ball randomly from the box, what would be the probability that the ball chosen is silver?

Step 6: Calculation for problem in Step 5

Since there is only one silver ball, and there are three balls in total, the probability is therefore \(\frac{1}{3}\), which is the desired outcome.