Ch 6 and 7 Review - Weebly



Ch 6 and 7 Review

Matching

Match each of these terms with one of the phrases below.

|a. |sample space |e. |outcomes |

|b. |empirical probability |f. |theoretical probability |

|c. |complement |g. |trials |

|d. |subjective probability |h. |event |

____ 1. the outcomes not included in a particular event

____ 2. based upon intuition and previous experience

Short Answer

3. Explain the differences between the empirical probability, theoretical probability, and subjective probability.

4. Explain the meaning of the terms in the probability formula, [pic].

5. Two coins are tossed simultaneously. What is the probability of tossing a head and a tail?

6. A standard die is rolled. What is the probability of rolling a prime number?

7. Two standard dice are rolled. What is the probability that the total of the two dice is less than 4?

8. Two standard dice are rolled. What is the probability that a sum less than 7 is not rolled?

9. If the odds are 9:1 against the next car you see being red, what proportion of cars in your area are red?

10. Participants in marathons are often given numbers to wear, so that race officials can identify individual runners more easily. If the numbers are assigned randomly, what is the probability that the eight fastest runners will finish in the order of their assigned numbers, assuming that there are no ties?

11. A bag contains three white marbles, five green marbles, and two red marbles. What are the odds in favour of randomly picking both red marbles in the first two tries? Assume that the first marble picked is not put back into the bag.

12. If the probability of the Rangers defeating the Eagles in a hockey game is [pic], what is the probability that the Rangers will win two consecutive games against the Eagles?

13. The probability that Jacqueline will be elected to the students’ council is 0.6, and the probability that she will be selected to represent her school in a public-speaking contest is 0.75. The probability of Jacqueline achieving both of these goals is 0.5.

a) Are these two goals mutually exclusive? Explain your answer.

b) What is the probability that Jacqueline is either elected to the students’ council or picked for the public-speaking contest?

c) What is the probability that she fails to be selected for either the students’ council or the public-speaking contest?

14. What does a probability distribution show?

15. What is the key characteristic of a continuous variable?

16. What is the difference between a discrete random variable and a continuous random variable?

17. What is a uniform probability distribution?

18. Classify the following random variables as discrete or continuous.

a) the number of times a player bumps the ball in a volleyball game

b) the length of time a student spends doing homework

c) the volume of water in a swimming pool

d) the number of blue cars on a highway

19. Explain whether counting the number of red cars parked on a street is a probability experiment that has a uniform probability distribution.

20. A die is rolled twenty times and the number of 1s is counted. Can this situation be modelled by a binomial distribution? Justify your answer.

21. Explain why P(X = 2) = P(X = 3) in a binomial distribution where n = 5 and p = 0.5.

Problem

22. If a committee of six is to be chosen randomly from nine grade-11 students and seven grade-12 students, what is the probability that the committee will be either all grade-12 students or all grade-11 students?

23. A survey of 50 female high-school athletes collected the following data.

|Team |Number of Athletes |

|Field hockey |23 |

|Volleyball |16 |

|Rugby |29 |

|Both rugby and field hockey |8 |

|Both rugby and volleyball |9 |

|Both field hockey and volleyball |7 |

|All three teams |6 |

a) Draw a Venn diagram to illustrate the above data.

b) Determine the probability that a randomly selected athlete from this sample will play either rugby or field hockey.

c) What is the probability that a randomly selected athlete will play on only one of the three sports teams?

d) Determine the probability that a randomly selected rugby player also plays volleyball.

e) Determine the probability that a randomly selected athlete who does not play rugby is on the field-hockey team.

24. A spinner has three equally-sized sectors, numbered 1 through 3.

a) What is the probability that the arrow on the spinner will stop on an even number?

b) What is the expected outcome?

Ch 6 and 7 Review

Answer Section

MATCHING

1. ANS: C REF: Knowledge & Understanding OBJ: Section 6.1

LOC: CP2.06 TOP: Probability concepts

2. ANS: D REF: Knowledge & Understanding OBJ: Section 6.1

LOC: CP2.06 TOP: Probability concepts

SHORT ANSWER

3. ANS:

Empirical probability is based on experimental results and direct observations of events.

Theoretical probability is based on mathematical calculations and the analysis of the possible outcomes.

Subjective probability is based on past experience or informed guesswork.

REF: Communication OBJ: Section 6.1 LOC: CP2.06

TOP: Probability concepts

4. ANS:

P represents probability.

A represents the event A.

The letter n stands for “number” and n(A) represents the number of outcomes in which event A occurs.

S represents the sample space, and n(S) is the number of outcomes in the sample space (the total number of possible outcomes).

REF: Communication OBJ: Section 6.1 LOC: CP2.06

TOP: Probability concepts

5. ANS:

[pic]

REF: Knowledge & Understanding OBJ: Section 6.1 LOC: CP2.01

TOP: Calculating probability

6. ANS:

[pic]

REF: Applications OBJ: Section 6.1 LOC: CP2.01 TOP: Calculating probability

7. ANS:

[pic]

REF: Applications OBJ: Section 6.1 LOC: CP2.01 TOP: Calculating probability

8. ANS:

[pic]

REF: Applications OBJ: Section 6.1 LOC: CP2.01 TOP: Calculating probability

9. ANS:

10%

REF: Applications OBJ: Section 6.2 LOC: CP2.06 TOP: Calculating odds

10. ANS:

[pic]

REF: Applications OBJ: Section 6.3 LOC: CP2.01 TOP: Calculating probability

11. ANS:

The probability of picking the two red marbles in the first two picks is [pic].

Therefore, the odds in favour of picking the two red marbles are 1:44.

REF: Applications OBJ: Section 6.4 LOC: CP2.01 TOP: Dependent and independent events

12. ANS:

[pic]

REF: Applications OBJ: Section 6.4 LOC: CP2.01 TOP: Dependent and independent events

13. ANS:

a) The two goals cannot be mutually exclusive since the probability of achieving both is 0.5.

b) 0.85

c) 0.15

REF: Applications, Communication OBJ: Section 6.5 LOC: CP2.01

TOP: Mutually exclusive events

14. ANS:

A probability distribution shows the probabilities of all possible outcomes of an experiment.

REF: Knowledge & Understanding OBJ: Section 7.1 LOC: CP2.03

TOP: Probability distribution concepts

15. ANS:

A continuous variable has an infinite number of different possible values in a continuous interval.

REF: Knowledge & Understanding OBJ: Section 7.1 LOC: CP2.02

TOP: Probability distribution concepts

16. ANS:

A discrete random variable has separated values while a continuous random variable has an infinite number of possible values along a continuous interval.

REF: Knowledge & Understanding OBJ: Section 7.1 LOC: CP2.02

TOP: Probability distribution concepts

17. ANS:

A uniform probability distribution is a distribution in which all outcomes are equally likely in any single trial.

REF: Knowledge & Understanding OBJ: Section 7.1 LOC: CP2.03

TOP: Probability distribution concepts

18. ANS:

a) discrete

b) continuous

c) continuous

d) discrete

REF: Knowledge & Understanding OBJ: Section 7.1 LOC: CP2.02

TOP: Probability distribution concepts

19. ANS:

The experiment does not have a uniform probability distribution because all colours of cars are not equally likely.

REF: Applications, Communication OBJ: Section 7.1 LOC: CP2.03

TOP: Probability distribution concepts

20. ANS:

Yes, there are a given number of independent trials and rolling a 1 is a success.

REF: Communication OBJ: Section 7.2 LOC: CP2.05

TOP: Binomial distribution concepts

21. ANS:

Since p = q and nCr = nCn–r, P(X = 2) = [pic] = P(X = 3).

REF: Applications, Communication OBJ: Section 7.2 LOC: CP2.05

TOP: Binomial probabilities

PROBLEM

22. ANS:

[pic]

REF: Applications OBJ: Section 6.5 LOC: CP2.01 TOP: Mutually exclusive events

23. ANS:

a)

[pic]

b) Only 6 athletes do not play either field hockey or rugby. Therefore, the probability of selecting an athlete who plays either sport is [pic] = 0.88.

c) From the Venn diagram, 38 athletes play on only one of the three sports teams. Therefore, P(only one team) = [pic], or 0.76.

d) Venn Diagram Method

The Venn diagram above shows that 9 volleyball players also play on the rugby team. Therefore, [pic].

Conditional Probability Method

[pic]

e) Venn Diagram Method

The Venn diagram above shows that 15 out of the 21 athletes not on the rugby team play field hockey. Therefore,

[pic]

Conditional Probability Method

[pic]

REF: Applications, Communication OBJ: Section 6.5 LOC: CP2.01

TOP: Mutually exclusive events

24. ANS:

a) The only even number on the spinner is 2, so the probability is [pic].

b) [pic]

REF: Applications OBJ: Section 7.1 LOC: CP2.03, CP2.04

TOP: Expected value

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