Question 8·Medium·Probability and Conditional Probability
The number of penguins in a zoo exhibit, sorted by gender and type of penguin, is shown in the table below.
| Type of penguin | Male | Female | Total |
|---|---|---|---|
| Chinstrap | 41 | 59 | 100 |
| Emperor | 8 | 27 | 35 |
| Gentoo | 49 | 54 | 103 |
| Macaroni | 42 | 40 | 82 |
| Total | 140 | 180 | 320 |
Which type of penguin has a female population that is the closest to being of the total female penguin population in the exhibit?
For table-and-fraction questions, first read the wording carefully to see which total is relevant (for example, total females vs. total penguins). Compute the required fraction of that total (here, of 180), then systematically compare each category’s value to that target by finding simple differences. Always check every option rather than stopping at the first one that seems close, so you reliably choose the one that is closest to the requested fraction.
Hints
Focus on the right total
The phrase " of the total female penguin population" refers to a total in the Female column. Which number at the bottom of that column is the total you should use?
Compute the target number
Once you know the total number of female penguins, multiply that number by . What number do you get?
Compare distances from the target
Look at the female counts for each penguin type. For each one, ask: how far is this number from the target value you just calculated? Which type has the smallest difference?
Desmos Guide
Find one-third of the total female count
In Desmos, type 180/3 and look at the numeric result. This is the number of females that represents one-third of the total female penguin population.
Compare each type to the target
On separate lines in Desmos, type expressions for the absolute differences, such as abs(59 - 180/3), abs(27 - 180/3), abs(54 - 180/3), and abs(40 - 180/3). Compare the outputs and identify which expression gives the smallest value; the corresponding penguin type is the answer.
Step-by-step Explanation
Identify the relevant total
The question asks for a female population that is closest to being of the total female penguin population.
From the table, the total number of female penguins is 180 (bottom of the Female column). This is the number you should use to find of the female population.
Find one-third of the total female population
Compute of 180:
So we are looking for the type of penguin whose female count is closest to 60.
Compare each type’s female count to 60
From the table, the female counts are:
- Chinstrap: 59
- Emperor: 27
- Gentoo: 54
- Macaroni: 40
Find how far each is from 60 (use absolute differences):
- Chinstrap:
- Emperor:
- Gentoo:
- Macaroni:
Choose the smallest difference
The smallest difference from 60 is 1, which comes from the Chinstrap penguins (59 females). Therefore, the type of penguin whose female population is closest to of the total female population is Chinstrap.