On the average, only 1 person in 1000 has a particular rare blood type. How many people would have to be tested to give a probability greater than 1/2 of finding at least one person with this blood type?

• 663
• 683
• 693
• 705
• 725

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Assume that, during each second, a Dartmouth switchboard receives one call with probability .01 and no calls with probability .99. Use the Poisson approximation to estimate the probability that the operator will miss at most one call if she takes a 5-minute coffee break.

• 0.85
• 0.875
• 0.9
• 0.925
• 0.95

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Assume that the probability that there is a significant accident in a nuclear power plant during one year's time is .001. If a country has 100 nuclear plants, estimate the probability that there is at least one such accident during a given year.

• 0.085
• 0.09
• 0.095
• 0.1
• 0.105

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

A royal family has children until it has a boy or until it has three children, whichever comes first. Assume that each child is a boy with probability 1/2. Find the expected number of boys in this royal family and the expected number of boys.

• 0.825
• 0.85
• 0.875
• 0.9
• 0.925

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Gerolamo Cardano in his book, The Gambling Scholar, written in the early 1500s, considers the following carnival game. There are six dice. Each of the dice has five blank sides. The sixth side has a number between 1 and 6---a different number on each die. The six dice are rolled and the player wins a prize depending on the total of the numbers which turn up. Find, as Cardano did, the expected total without finding its distribution.

• 3
• 3.25
• 3.5
• 3.75
• 4

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

The probability function for the claim frequency is given below

What is the probability that the claim frequency will lie within one standard deviation of the mean of the claim frequency distribution?

1. 0.1631
2. 0.4694
3. 0.6231
4. 0.6689
5. 0.8011

A hospital receives 1/5 of its flu vaccine shipments from Company X and the remainder of its shipments from other companies. Each shipment contains a very large number of vaccine vials.

For Company X’s shipments, 10% of the vials are ineffective. For every other company, 2% of the vials are ineffective.

The hospital tests 30 randomly selected vials from a shipment and finds that one vial is ineffective.

Calculate the probability that this shipment came from Company X.

• 0.10
• 0.14
• 0.37
• 0.63
• 0.86

A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% chance of achieving a high performance level during the coming year. The events of different employees achieving a high performance level during the coming year are mutually independent.

Calculate the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance.

• 24
• 30
• 40
• 60
• 120

A large pool of adults earning their first driver’s license includes 50% low-risk drivers, 30% moderate-risk drivers, and 20% high-risk drivers. Because these drivers have no prior driving record, an insurance company considers each driver to be randomly selected from the pool.

This month, the insurance company writes four new policies for adults earning their first driver’s license.

Calculate the probability that these four will contain at least two more high-risk drivers than low-risk drivers.

• 0.006
• 0.012
• 0.018
• 0.049
• 0.073

A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is 0.60. The numbers of accidents that occur in different months are mutually independent.

Calculate the probability that there will be at least four months in which no accidents occur before the fourth month in which at least one accident occurs.

• 0.01
• 0.12
• 0.23
• 0.29
• 0.41