## D.16 Answers: Probability

Answers to exercises in Sect. 16.8.

Answer to Exercise 16.1: 1. Probability draw a King: $$4/52 = 0.07692$$. 2. Odds draw a King: $$4/48 = 0.08333$$. 3. Probability draw a picture card: $$16/52 = 0.3077$$. 4. Odds draw a picture card: $$16/(52 - 16) = 0.4444$$. 5. Not independent. This is like Example 16.10. 6. Are independent. What happens on the die does not change what happens with the cards.
Answer to Exercise 16.2: Only a 50–50 chance if the events were equally likely… they clearly are not.
Answer to Exercise 16.3: 1. $$9/16$$; about 56.3%. 2. $$6/57$$; about 0.105. (Or, 10.5% if expressed as a percentage.) 3. The number of pilots in each age group.
Answer to Exercise 16.4: 1. Not independent events: If it rains, less likely to walk to work than if it doesn’t rain. 2. Not independent events: A smoker is far more likely to suffer from lung cancer than a non-smoker. 3. Independent events: My rubbish is collected, rain or not.

Answer to Exercise 16.5: 1. Expect $$100\times 0.99 = 99$$ people to return a positive test result. 2. Expect $$100\times (1 - 0.98) = 2$$ people to return a positive test result.

A positive test result may or may not mean the person has the disease.
Answer to Exercise 16.6: The reasoning assumes that the three outcomes (HH, TT, HT) are equally likely, which is not true. For example, consider tossing a 20-cent coin (shown in lower-case, normal font) and a 1-dollar coin (shown in capitals, bold font). The four outcomes are: hH, hT, tH tT.