WU Probability of An Event Occurring and Not Occurring Questions

• Define each of the following terms in your own words and provide an example: 

1. Bias 
2. Odds 
3. Favourable outcome
4. Data

• Describe in words (do not list all elements) the sample space of each experiment, find how many elements it contains, and state one of the elements: 

1. Drawing two cards from a deck without replacement. 
2. Drawing three cards from a deck with replacement. 
3. Rolling a 6-sided die, then flipping that many coins. 

• Find the theoretical probability of: 

1. Drawing a red ace or a heart from a regular deck of cards.
2. When guessing the birthdays of two friends, getting exactly one right, if you know the first friend was born in a leap year and the second friend wasn’t. Assume birthdays are evenly distributed through the year. 
3. Being dealt at least 4 hearts in a hand of 5 cards dealt from a regular deck. 
4. When selecting 3 cards from a regular deck without replacement, having the 3rd card be the second spade drawn. 

• Manpreet and her friends meet every Thursday night to play a different sport. When they play basketball, she has a 75% chance of being on the winning team. Considering their game next week, if there is a 40% chance they will play basketball then what are the odds in favour of Manpreet being on the winning team of a basketball game? 
• A modified deck of cards is created by removing the 9s and 10s, and the red aces, from a regular deck. 

1. How many cards are in this deck? 
2. Given that an 8-card hand has been dealt from this deck, what is the probability of having exactly 3 hearts, 2 diamonds, 2 spades, and 1 club? 
3. When drawing two cards from this deck without replacement, what are the odds against getting a pair (two cards of the same rank)? 

• If you roll a 6-sided die 5 times and get the result “1, 1, 1, 1, 1” can you conclude whether the die is “fair” or not? Explain. 
• In the field of statistics, give an example of: 

1. A discrete variable. 
2. A continuous variable. 
3. A qualitative variable. 

• Is it ever ethical to add bias to a statistical study? In a paragraph, why or why not?
• You are conducting a statistical survey of library users. There are approximately 2500 people in the population (library patrons in a month), and you have a full list of their names, phone numbers, addresses, time & date of last visit, and any other reasonable information. If you want to create and survey a fair sample of 25 people, describe how you could do so using the following techniques. Be sure to include how you would contact your subjects. 

1. Simple random sampling 
2. Systematic random sampling
3. Stratified random sampling 
4. Cluster random sampling
5. Multistage random sampling 

• A supermarket conducted a survey of 1000 consumers. Their population was “adults who shop for groceries.” Use specific examples to explain how the following biases could have had the following effects: 

1. How could sampling bias have made it seem like adults eat more bread than in reality? 
2. How could non-response bias have made it seem like adults eat less fruit than in reality? 
3. How could response bias have made it seem like adults eat more vegetables than in reality? 
4. How could measurement bias have made it seem like adults drink more coffee than in reality? 

• In a recent survey of a fair stratified random sample of the population, a question appeared as:
  Do you plan to vote in favour of the speed limit change? Yes/NoItalic text End
  Italic text startA scientist found the following number of responses per stratum: 

Age 20-24 Age 25-29 Age 30-34

Yes 45 80 5

No 25 25 15

No response 25 10 55

1. What are two reasons a respondent might not answer this question? 
2. What are the strata in this sample? 
3. If a person is picked at random from the sample, what is the probability that they are age 25-29 or did not respond to this question? 
4. If three people are picked at random from the sample, what is the probability that at least one did not respond to this question? 
5. If we assume there is no bias, what conclusions can be drawn about the population’s opinion of the speed limit change? Justify your response. 
6. How would your answer to (e) change if we found out that 90% of those who did not respond are actually against the change?