7 - Mr. Roy Math Superior CVI - Home



7.1 Probability Distributions

McGraw-Hill Ryerson Mathematics of Data Management, pp. 369–377

1. What is the expected outcome of a fair game? Include an example of a fair game.

2. Outline an experiment that has a uniform probability distribution and use it to show that the sum of the probabilities is 1.

3. A Random Draw lottery has sold $52 000 000 worth of tickets, with each ticket sold for $5.00. The prizes and their frequencies are shown in the following table.

|Prize ($), x |Number of Prizes |P(x) |

|12 000 000.00 |1 | |

|206 955.00 |5 | |

|2408.00 |25 | |

|147.00 |100 | |

|100.00 |1 000 | |

|10.00 |5 000 | |

a) How many tickets were sold?

b) Complete the column, P(x).

c) What is the expected prize per ticket?

d) What is the expected profit per ticket?

4. a) In a family with three children, determine the probability distribution for the number of boys.

b) What is the expected number of boys?

5. Which die has the higher expectation?

A: a four-sided die with its faces numbered 6, 12, 18, and 24

B: a six-sided die with its faces numbered 4, 8, 12, 16, 20, and 24

7.2 Binomial Distributions

McGraw-Hill Ryerson Mathematics of Data Management, pp. 378–387

1. What are the characteristics of a binomial distribution?

2. Prepare a table and a graph for a binomial distribution with p = 0.4 and n = 10.

3. A salesperson estimates that 30% of the people who come into the store make a purchase. Find the binomial distribution for the number of sales if 10 people come into the store.

4. A basketball player makes foul shots 78% of the time. In a game, the player has six foul shot attempts. What is the expected number of baskets?

5. A department store prints scratch-and-save discount coupons to distribute to its customers. The numbers for each percent discount are shown in the table.

|Percent |Number of Each Type of Discount Available|

|Discount | |

|60% |50 |

|50% |25 000 |

|30% |50 000 |

|10% |500 000 |

Determine the expected percent discount.

6. An examination consists of 50 multiple-choice items, each with 4 possible answers. What is the probability of guessing 25 or more correct answers?

7. A bank found that 25% of its loans to new small businesses become delinquent. Ten small businesses are selected randomly from the bank’s files.

a) What is the probability that three of them are delinquent?

b) What is the probability that at least three of them are delinquent?

c) What is the expected delinquency?

7.3 Geometric Distributions

McGraw-Hill Ryerson Mathematics of Data Management, pp. 388–396

1. Explain why rolling a die until a 3 shows can be modelled by a geometric distribution.

2. In a shoot out in a hockey competition, a player scores on 80% of his shots.

a) What is the probability that the player will not miss the goal until his tenth try?

b) What is the expected number of shots before he misses?

3. A factory producing electric motors has a 0.2% defective rate. A quality control inspector tests randomly selected motors from this production line.

a) What is the probability that the first defective motor will be the sixth one tested?

b) What is the probability that the first defective motor will be among the first six tested?

c) What is the expected waiting time before the first defective motor is tested?

4. A computer has been programmed to generate a list of random numbers between 1 and 50.

a) What is the probability that the number 20 will not appear until the 12th number?

b) What is the expected number of trials until a 20 appears?

5. In order to start a particular board game, a player must roll a 1 or a 6. Show the probability distribution for the number of rolls required to start, up to 10 rolls.

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