Question 1

Answer the following questions with a partner:

1. If it is snowing, what is the probability someone will ride their bike?
2. If you know someone holds one  political belief, how likely are they to hold a conflicting political belief?
   
   Credit: iStock/FatCamera

Question 2

Use the table to estimate the following probabilities:

1. The probability that a person thinks the United States spends too much on childcare
2. The probability that a person thinks the United States spends about the right  amount on both childcare and developing alternative energy resources
3. The probability that a person thinks the United States spends about the right  amount developing alternative energy resources and too much on childcare

Question 3

The previous questions asked about people in general, so the denominator was the  total number of people in the survey (2,199). Now, let’s focus on the people who  think the United States spends too little on childcare.

1. What is the new denominator if we focus on the people who think the United  States spends too little on childcare?
2. What is the probability that a person believes the United States spends too  little on developing alternative energy resources GIVEN they think the United  States spends too little on childcare?

Question 4

Use the previous table to estimate the following conditional probabilities:

1. The probability that a randomly selected person thinks the United States spends too much on childcare GIVEN they think the United States spends  about the right amount developing alternative energy resources
2. The probability that a randomly selected person thinks the United States spends about the right amount developing alternative energy resources  GIVEN they think the United States spends too much on childcare

Question 5

Every day, Jade recorded whether she drank bubble tea, café sua da, both, or  neither. On 5% of days, she drank both bubble tea and café sua da. On 35% of  days, she drank café sua da and did not drink bubble tea. On 20% of days, Jade  drank bubble tea. On 80% of days, Jade did not drink bubble tea.

1. Assume Jade’s data are from the last 100 days. This means she drank both  café sua da and bubble tea on 0.05 * 100 = 5 days. Use this information to  complete the following table.

   	Drinks bubble tea	Does not drink bubble tea	Total
   Drinks café sua da	5
   Does not drink café sua da
   Total	20

2. The probability of Jade not drinking bubble tea on a randomly selected day  is [latex]\frac{(35+45)}{100} = 0.80[/latex], or 80%. What is the probability of Jade drinking  bubble tea on a given day?
3. On a randomly selected day, what is the probability that Jade drinks  café sua da?
4. What is the probability of Jade drinking bubble tea AND café sua da on the  same randomly selected day?
5. What is the probability of Jade drinking bubble tea GIVEN she drank café  sua da?

   Formula for Conditional Probability
   For any events A and B where [latex]P(B) > 0[/latex],

   [latex]P(A GIVEN B) = \frac{P(A AND B)}{P(B)}[/latex]

    

6. Use the formula above to check your answer to Part E.
   Recall that two events are independent if [latex]P(A) GIVEN B) = P(A).[/latex]
   Alternatively, two events are independent if [latex]P(A) * P(B) = P(A AND B).[/latex]
7. Can we say that these two events—drinking bubble tea and drinking  café sua da—are independent? Explain.
8. Can we say that these two events—drinking bubble tea and drinking  café sua da—are independent? Explain.

Question 6

Consider two events A and B with [latex]P(A) > 0[/latex] and [latex]P(B) > 0[/latex]. Can A and B be both  mutually exclusive AND independent? Explain.