Answer:
Question 1: The probability that a bus is owned by Jerry, given that it runs on time:
Question 2: The probability that a bus is owned by Jerry, given that it runs late
Explanation:
A two-way table is very good to deal with these kind of probability questions because helps you to determine the every subset.
I will guide you on how to build the two-way table.
Identify the possible sets. These are:
- Buses operated within a particular town (100)
- Buses that run on time
- Buses that run late
- Buses owned by Jerry
- Buses not owned by Jerry.
With that, you start to build your table:
<u>1. Start</u>
Run on time Run late Total
Owned by Jerry
Not owned by Jerry
Total 100
Now, lets fill using each statement:
<u>2. 48 usually run on time</u>
Run on time Run late Total
Owned by Jerry
Not owned by Jerry
Total 48 100
<u>3. 36 of these are owned by Jerry:</u>
Run on time Run late Total
Owned by Jerry 36
Not owned by Jerry
Total 48 100
<u />
<u>4. Of the 52 buses that usually run behind, only 7 are owned by Jerry:</u>
Run on time Run late Total
Owned by Jerry 36 7 43
Not owned by Jerry
Total 48 52 100
You may even fill the second row, but you will not need it to answer the questions.
<u>5. Complete the table using differences:</u>
Run on time Run late Total
Owned by Jerry 36 7 43
Not owned by Jerry 12 45 57
Total 48 52 100
<u>6. Answer the questions:</u>
<u>Question 1</u>: The probability that a bus is owned by Jerry, given that it runs on time:
- Probability of an event = # favorable outcomes / # total outcomes
- Probability that a bus owned by Jerry, given that it runs late = # buses owned by Jerry that runs on time / # buses that run on time = 36 / 48 = 3/4
<u>Question 2</u>: The probability that a bus is owned by Jerry, given that it runs late
- Probability that a bus is owned by Jerry, given that it runs late = # buses owned by Jerry that run late / # buses that run late = 7 / 52
