Question 13·Easy·Probability and Conditional Probability
The table summarizes the responses of 799 randomly selected US teens about how often they talk on a cell phone and their texting behavior.
| Texting behavior | Talks on cell phone daily | Does not talk on cell phone daily | Total |
|---|---|---|---|
| Light | 110 | 146 | 256 |
| Medium | 139 | 164 | 303 |
| Heavy | 166 | 74 | 240 |
| Total | 415 | 384 | 799 |
If one of the 799 teens surveyed is selected at random, what is the probability that the teen talks on a cell phone daily?
For two-way tables, first identify exactly what event the question is asking about (here, “talks on a cell phone daily” regardless of texting behavior). Use the appropriate row or column total for that event as the numerator, and use the grand total of all individuals as the denominator. Avoid mixing up row totals with column totals, and watch out for choosing the complement (the opposite event) by mistake.
Hints
Connect the question to the table
You are asked for the probability that a randomly selected teen talks on a cell phone daily. Which part of the table tells you how many teens have that characteristic?
Think about the denominator
Probability is (number with the characteristic) divided by (total number of teens). Where in the table do you find the total number of teens surveyed?
Use the correct total for daily talkers
To get how many teens talk on a cell phone daily, look at the column total for "Talks on cell phone daily," not just one texting category.
Write the fraction
Once you know the total number of teens and the total number who talk on a cell phone daily, place the daily-talkers count over the total number surveyed to form the probability.
Desmos Guide
Compute the probability as a decimal
In Desmos, type the fraction with the numerator equal to the column total under "Talks on cell phone daily" and the denominator equal to the grand total (799). The value Desmos outputs is the probability as a decimal; you can compare this to the answer choices written as fractions.
Step-by-step Explanation
Recall how to compute probability from a table
For equally likely outcomes, a probability is
Here, each of the 799 teens is one outcome.
Find the total number of teens surveyed
Look at the bottom-right cell of the table labeled Total. This gives the total number of teens surveyed: . This is the denominator of the probability.
Identify the number of teens who talk on a cell phone daily
The event we care about is "talks on a cell phone daily," regardless of texting behavior.
So we need everyone in the Talks on cell phone daily column:
- Light: 110
- Medium: 139
- Heavy: 166
The table already adds these for us in the Total row under that column: teens talk on a cell phone daily.
Form the probability as a fraction
Now divide the number of favorable outcomes (teens who talk on a cell phone daily) by the total number of teens surveyed:
So the correct answer is , which corresponds to choice B.