Question 19·Easy·Probability and Conditional Probability
The table gives the distribution of votes for a new school mascot and grade level for 80 students.
| Mascot | Sixth | Seventh | Eighth | Total |
|---|---|---|---|---|
| Badger | 4 | 9 | 9 | 22 |
| Lion | 9 | 2 | 9 | 20 |
| Longhorn | 4 | 6 | 4 | 14 |
| Tiger | 6 | 9 | 9 | 24 |
| Total | 23 | 26 | 31 | 80 |
If one of these students is selected at random, what is the probability of selecting a student whose vote for the new mascot was for a lion?
For table-based probability questions, first translate the event into a specific row and/or column in the table (here, "voted for lion" is one entire row). Use the grand total in the bottom-right as your denominator unless the question says "given" some condition, which would change the denominator. Form the fraction (favorable outcomes over total outcomes), then simplify it and match it to the answer choices, watching out for answers that use only part of the table as the denominator.
Hints
Focus on the correct row
Look at the table and find the row that corresponds to students who voted for lion. How many students are in that row in total?
Use the total number of students
What number in the table tells you how many students there are altogether? This is the total number of possible outcomes when one student is chosen at random.
Recall the basic probability formula
Probability of an event is . Use this idea with the lion votes and the total number of students.
Think about simplifying the fraction
Once you form the fraction for the probability, see if you can divide the numerator and denominator by the same number to simplify it.
Desmos Guide
Compute and simplify the fraction in Desmos
In Desmos, type 20/80 into the expression line. Look at the simplified fraction or decimal that Desmos shows; that value is the probability of selecting a student who voted for lion.
Step-by-step Explanation
Identify the event described
The problem asks for the probability of selecting a student whose vote was for a lion. So the event is "student voted for lion," regardless of grade level.
Find the number of favorable outcomes
Look at the row labeled Lion in the table. Add the numbers across that row (or use the row total given):
- Sixth: 9
- Seventh: 2
- Eighth: 9
The row total is already given as 20, so there are 20 students who voted for lion.
Find the total number of possible outcomes
The total number of students is given in the bottom-right corner of the table as 80. This means there are 80 possible students that could be chosen.
Write and simplify the probability
Probability is
Now simplify by dividing numerator and denominator by 20:
So the correct answer is , which corresponds to choice C.