Probability I: Introductory Ideas

Determine the probability of the following events in drawing a card from a standard deck of 52 cards.

During a recent bridge game, once the lead card had been played and the dummy's hand revealed, the declarer took a moment to count up the number of cards in each suit with the results given below.

Below is a frequency distribution of annual sales commissions from a survey of 300 media salespeople.

General Buck Turgidson is preparing to make his annual budget presentation to the U.S. Senate and is speculating about his chances of getting all or part of his requested budget approved. From his 20 years of experience in making these requests, he has deduced that his chances of getting between 50 and 74 percent of his budget approved are twice as good as those of getting between 75 and 99 percent approved, and two and one-half times as good as those of getting between 25 and 49 percent of his budget being approved. Finally, the entire budget has been approved only once during the general's tenure, and the general those not expect this pattern to change.

The office manager of an insurance company has the following data on the functioning of the copiers in the office:

Copier	Days Functioning	Days Out of Service
1	209	51
2	217	43
3	258	2
4	229	31
5	247	13

What is the probability of a copier being out of service based on these data?

Solution

Classify the following probability estimates as classical, relative frequency, or subjective:

The probability the Cubs will win the World Series this year is 0.175.
The probability tuition will increase next year is 0.95.
The probability that you will win the lottery is 0.00062.
The probability a randomly selected fl ight will arrive on time is 0.875.
The probability of tossing a coin twice and observing two heads is 0.25.
The probability that your car will start on a very cold day is 0.97.

Solution

Frome the following Venn diagram, which indicates the number of outcomes of an experiment corresponding to each event and number of outcomes that do not correspond to either event, give the probabilities indicated.

An inspector of the Alaska pipeline has the task of comparing the reliability of two pumping stations. Each stations is susceptible to two kinds of failure: pump failure and leakage. When either occur, the station must be shut be down. The data at hand indicate that the following probability prevail:

From the following Venn diagram, which indicates the number of outcomes of an experiment corresponding to each event give the probabilities indicated:

Using this Venn diagram, give the probabilities indicated:

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Probability I: Introductory Ideas

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