Question 25·Easy·Probability and Conditional Probability
Each of 157 gemstones can be classified as one of three classifications, as shown in the frequency table.
| Classification | Frequency |
|---|---|
| color X | 119 |
| color Y | 3 |
| color Z | 35 |
If one of the gemstones is selected at random, what is the probability of selecting a gemstone of color Y?
For probability questions with tables, go straight to the row that matches the event described (here, color Y), take its frequency as the number of favorable outcomes, and divide by the total frequency given (or the sum of all rows if not stated). Avoid mixing up events by double-checking that the numerator in your fraction comes from the correct category and that the denominator is the overall total, not just a part of the table.
Hints
Use the definition of probability
Think about how to express the probability of an event using the number of favorable outcomes and the total number of outcomes.
Identify the relevant counts in the table
Which number in the table tells you how many gemstones are color Y? Which number represents the total number of gemstones?
Form the fraction
Once you know the number of color Y gemstones and the total number of gemstones, place them into the fraction and then look for that fraction in the answer choices.
Desmos Guide
Compute the fraction value
In Desmos, type 3/157 and press Enter to see its decimal value. You will compare this to the decimals of the other answer options in the next step.
Compare and identify the matching choice
On separate lines, type 35/157, 119/157, and 154/157. Compare their decimals to 3/157. The fraction 3/157 matches option C, which is the correct answer.
Step-by-step Explanation
Recall the basic probability formula
For a situation where all outcomes are equally likely, the probability of an event is:
Here, the "event" is selecting a gemstone of color Y.
Identify the total number of outcomes
From the table, there are 157 gemstones in total. That is the total number of outcomes when one gemstone is selected at random.
Identify the number of favorable outcomes
The favorable outcomes are the gemstones of color Y.
From the table, there are 3 gemstones of color Y. So the number of favorable outcomes is 3.
Compute the probability and match it to a choice
Use the probability formula with 3 favorable outcomes and 157 total outcomes:
Now look at the answer choices and select the one that equals , which is choice C.