Question 16·Easy·Probability and Conditional Probability
The table summarizes members of a local organization by age group and whether they live east or west of the river.
| Live east of the river | Live west of the river | Total | |
|---|---|---|---|
| Less than 40 years old | 17 | 11 | 28 |
| At least 40 years old | 18 | 89 | 107 |
| Total | 35 | 100 | 135 |
If a member of the organization is selected at random, what is the probability that the selected member is at least 40 years old?
For table-based probability questions, first translate the wording into "numerator over denominator": identify exactly which group the question is asking about (here, "at least 40 years old") and use that group's total as the numerator, then use the grand total in the table as the denominator. Watch out for distractors that use the wrong row (such as the opposite age group) or the wrong column (such as east vs. west), and always check that your fraction matches the intended condition, not just any number from the table.
Hints
Focus on the correct row
Look at the row labeled "At least 40 years old". You want the total number in that entire row, not just east or west.
Remember how probability is defined
Probability of an event is . Identify both of these numbers from the table.
Use the grand total
Make sure the denominator of your fraction uses the overall total number of members from the bottom-right of the table, not just one column or one row total.
Desmos Guide
Confirm the fraction in Desmos
In the Desmos expression line, type the fraction using the values from the table as (number_at_least_40)/(total_number_of_members) and let Desmos simplify it or show the decimal value. Compare that result to the answer choices to see which fraction matches.
Step-by-step Explanation
Identify what the probability is asking for
The event we care about is: "member is at least 40 years old".
So we need:
- Numerator: the number of members who are at least 40 years old.
- Denominator: the total number of members in the organization.
Read the correct counts from the table
From the row labeled "At least 40 years old", the total number of such members is 107.
From the bottom-right corner of the table (the overall total), the total number of members in the organization is 135.
Write the probability as a fraction
Probability is
So the correct answer is .