Probability and sampling

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. Two fair dice are rolled. Find the probability that the sum is 2.
  2. A fair die is rolled 2 times. Find the probability of at least one six.
  3. The probability that a flight is late is 0.78. Find the probability that it is not late.
  4. A fair coin lands heads 7 times in a row. What is the probability of heads on the next toss?
    1. 1/2: the coin has no memory
    2. Less than 1/2: tails is due
    3. More than 1/2: heads is on a streak
  5. What does it mean that the probability of rain tomorrow is 0.7?
    1. On many days like tomorrow, it rains on about 70% of them
    2. It will rain for 70% of the day
    3. It will rain if the probability is above 0.5
  6. To simulate a free throw made with probability 0.6 using random digits 0–9, how many of the ten digits should stand for 'made'?
  7. 12% of a population has a condition. A test is positive for 86% of people with the condition and for 11% of people without it. Find P(positive).
  8. 22% of a population has a condition. A test is positive for 81% of people with the condition and for 12% of people without it. Find P(condition | positive).
  9. A disease affects 1 in 1,000 people. A test is 93% accurate for both sick and healthy people. Your test is positive. What is most likely?
    1. You are still more likely healthy: false positives from the many healthy people outnumber the true positives
    2. You are about 93% likely to be sick
    3. You are certainly sick
  10. A researcher measures the sleep of 376 randomly chosen teenagers and finds a mean of 7.1 hours. What is 7.1?
    1. A statistic: it describes the sample
    2. A parameter: it describes all teenagers
    3. The population
  11. To learn how much US college students spend on books, a team surveys 671 students at 20 colleges. What is the population?
    1. All US college students
    2. The 671 students surveyed
    3. The 20 colleges
  12. Census records show that 52% of all households in a town own a car. What is 52%?
    1. A parameter: it describes the whole population
    2. A statistic
    3. A sample proportion