Question 20·Medium·Probability and Conditional Probability
For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results are summarized in the table below.
| Rain | No rain | Total | |
|---|---|---|---|
| Number of weekdays | 12 | 48 | 60 |
| Number of weekend days | 8 | 16 | 24 |
| Total | 20 | 64 | 84 |
If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?
For two‑way tables and conditional probability questions, first underline or note the condition (after the word “if” or “given”) to decide which row or column defines your denominator. Then, within that restricted row/column, pick out the count that matches the specific category asked about for your numerator. Write the probability as (desired cell)/(conditional total) and simplify the fraction; this avoids mixing up unconditional and conditional probabilities, a common SAT trap.
Hints
Focus on the condition in the question
The phrase "If one of the days on which there was no rain is selected" tells you that you should only consider the column labeled No rain. Do not use the total number of days in the whole table as your denominator.
Locate the correct counts in the table
In the No rain column, how many total days are there? Among those, how many are weekend days?
Form and simplify the probability
Write the probability as a fraction: (weekend days with no rain) over (all days with no rain). Then simplify that fraction by dividing numerator and denominator by a common factor.
Desmos Guide
Use Desmos to compute and simplify the fraction
In Desmos, type 16/64 into an expression line. Desmos will show the simplified fraction; that simplified value is the probability that a randomly chosen no‑rain day was a weekend day.
Step-by-step Explanation
Identify what the question is asking
The question says: If one of the days on which there was no rain is selected at random... This means we are only choosing from days in the No rain column, not from all 84 days. We want the probability that such a day is a weekend day.
Pull the relevant numbers from the table
From the table:
- Total number of no‑rain days (all days with no rain) is .
- Number of weekend days with no rain is .
These are the only two numbers we need to form the probability.
Write the conditional probability as a fraction
The probability we want is:
- favorable outcomes: weekend days with no rain
- possible outcomes: all no‑rain days
So the probability is
Simplify the fraction to get the final probability
Now simplify by dividing numerator and denominator by :
So, the probability that a randomly selected no‑rain day was a weekend day is .