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. \(6/457\); about 10.5%.
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.