Question 1

Rafael travels to work each day either by bus or by bike. We have data from 100 of  Rafael’s trips to work.

1. Use the row and column totals to complete the table below.

   	Bike	Bus	Total
   Rain	5		20
   No Rain		20	80
   Total	65	35	100

2. Calculate the probability that on a randomly selected day it rains AND Rafael  rides his bike. Round to the nearest hundredth.
3. Calculate the probability that on a randomly selected day Rafael rides his  bike GIVEN it rains. Round to the nearest hundredth.
4. You work with Rafael but have different shifts. You arrive at work at 6 AM  and Rafael arrives at work at noon. Once Rafael arrives, you overhear him  say that he rode his bike to work. What is the probability that it is raining? Round to the nearest hundredth.
5. You work with Rafael but have different shifts. You arrive at work at 6 AM  and Rafael arrives at work at noon. Once Rafael arrives, you overhear him  say that he rode the bus to work. What is the probability that it is raining?  Round to the nearest hundredth.

Question 2

Mali travels to work each day either by walking or riding her bike. It turns out that  15% of the days are rainy. On a rainy day, there is an 80% chance she walks to  work. If it is not raining, there is a 30% chance she walks to work.

On Monday, you have no idea whether it’s raining or not. Then Mali walks into work  with her bike helmet, which tells you she biked to work. What is the probability that it  is raining?

We are provided the probability that Mali walks to work given it is raining, but we  want to calculate the probability that it is raining given she biked to work.

In this question, we are not given the table to directly answer the questions, so one  common problem-solving strategy is to create a table using a hypothetical number of  responses.

In Parts a through i, use a hypothetical sample of 1,000 days. Note that you could  use any hypothetical number of days, but using a number like 1,000 usually makes  the calculations easier.

1. As you work through the remaining parts of this question, complete the table.

   	Bike	Walk	Total
   Rain
   No Rain
   Total			1,000

2. Use the given information “15% of the days are rainy” to calculate the value  and add it to the table.
3. Use the given information “On a rainy day, there is an 80% chance she  walks to work” to calculate the value and add it to the table.
4. Use the answers to Parts B and C to calculate the number of days it rains  AND she bikes.
5. Calculate the number of days that there is no rain.
   Hint: The row totals should add up to 1,000.
6. Use the given information “If it is not raining, there is a 30% chance she  walks to work” to calculate the value and add it to the table.
7. Calculate the number of days it does not rain AND she bikes.
8. Fill in the two remaining cells of the table.
9. Finally! Answer the original question:

   On Monday, you have no idea whether it’s raining or not. Then Mali walks  into work with her bike helmet, which tells you she biked to work. What is the  probability that it is raining? Round to the nearest hundredth.