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Chapter 6 - Probability
Things You Should Know
1. Probability
a) The probability of an event must be in the range from 0 to 100%.
b) Theoretical Probability: [pic]
c) Empirical Probability: In an experiment, the number of times an event occurs divided by the number of trials.
d) Probability of a compliment of an event (an event doesn’t occur) [pic]
2. Odds
a) Odds in favour of an event A are given by: [pic]
b) Odds against an event A are given by: [pic]
c) If the odds in favour of A are [pic], the probability of event A occurring is [pic]
3. “AND” Events
a) If A and B are independent events, the probability of both occurring is given by:
[pic]
b) If event B is dependent on event A, the conditional probability of both events is:
[pic]
4. “OR” Events
a) If A and B are mutually exclusive (cannot both happen) events, the probability of either A or B occurring is: [pic]
b) If A and B are non-mutually exclusive events, then the probability of either A or B or both events occurring is: [pic]
Chapter 6 Practice
1. Two identical spinners each have five equal sectors that are numbered 1 to 5. What is the probability of a total of 7 when you spin both these spinners?
2. Tom is practicing archery with a target that has three concentric zones: a circular bull’s-eye in the centre, an inner ring, and an outer ring. He has a 0.12 probability of hitting the bull’s-eye, a 0.37 probability of hitting the inner ring, and a 0.43 probability of hitting the outer ring. On an given shot, what is the probability that Tom
a) Misses the target?
b) Hits the target but does not get a bull’s-eye?
c) Hits the inner ring or the bull’s-eye?
3. The probability of Jim hitting the bull’s-eye on a dart board is 0.04. What are the odds in favour of Jim not hitting the bull’s-eye?
4. What are the odds in favour of a total greater than 9 in a given roll of two standard dice?
5. If a bowl contains ten hazelnuts and eight almonds, what is the probability that four nuts randomly selected from the bowl will all be hazelnuts?
6. If a CD player is programmed to play the CD tracks in random order, what is the probability that it will play six songs from a CD in order from your favourite to your least favourite?
7. A six-member working group to plan a student common room is to be selected from five teachers and nine students. If the working group is randomly selected, what is the probability that it will include at least two teachers?
8. Leela has five white and six grey huskies in her kennel. If a wilderness expedition chooses a team of six sled dogs at random from Leela’s kennel, what is the probability the team will consist of
a) Exactly two white huskies?
b) All grey huskies?
c) Three of each colour?
9. Suppose you simultaneously roll a standard die and spin a spinner that is divided into 10 equal sectors, numbered 1 to 10. What is the probability of getting a 4 on both the die and the spinner?
10. Carrie is a kicker on her rugby team. She estimates that her chances of scoring on a penalty kick during a game are 75% when there is no wind, but only 60% on a windy day. If the weather forecast gives a 55% probability of windy weather today, what is the probability of Carrie scoring on a penalty kick in a match this afternoon?
11. If 28% of the population of Statsville wears contact lenses, 37% have blue eyes, and 9% are blue-eyed people who wear contact lenses, what is the probability that a randomly selected resident has neither blue eyes nor contact lenses?
12. Steve estimates that he has a 65% chance of passing Math and a 70% chance of passing English. Assuming that Math and English are independent events,
a) What is the probability that Steve will pass Math but fail English?
b) What is the probability that Steve fails both subjects?
c) What is the probability that Steve passes both subjects?
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Where n(A) is the number of ways a given event can occur and n(S) is the total number of possible events.
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