# Math assignment 8

**Paper, Order, or Assignment Requirements**

Written assignments For each assignment, do the starred exercise and one other exercise of your choice. The answer to the required exercise should be in WP, but calculations in other exercises can be by hand. ——————-

**Assignment VIII**

- Solve one of the following:

In *Letter to a Friend on Sets in Court Tennis *(written 1687, published 1713), Jakob Bernoulli analyzed the probabilities at any point in a game or set of court tennis, whose scoring rules are virtually identical with those of tennis today. He determined the odds both when the players were evenly matched and when one player was stronger than the other.

If two players A and B are evenly matched in a tennis tame with the score 15:30, determine the probability of player A winning (remembering that one must win by two points).

Suppose that the probability of success in an experiment is 1/10. How many trials of the experiment are necessary to ensure even odds on it happening at least once? Calculate both by De Moivre’s exact method and his approximation.

How many throws of three dice are necessary to ensure even odds that three ones will occur at least once?

In a lottery in which the ratio of the number of losing tickets to the number of winning tickets is 39:1, how many tickets should one buy to give oneself even odds of winning a prize?

- With interest at 4%, what is the present value of an annuity of one pound per year for 50 years?

- From Newton’s
*Universal Algebra*solve one of the following:

Of three workmen, A can finish a given job once in three weeks, B can finish it three times in eight weeks, while C can finish it five times in twelve weeks. How long will it take for the three workmen to complete the job together?

Or

Given the perimeter *a* and the area *b ^{2}* of a right triangle, find its hypotenuse.

- From Maclaurin’s
*Treatise of Algebra*solve one of the following:

Suppose that the distance between London and Edinburgh is 360 miles and that a courier for London sets out from the Scottish city running at 10 mph at the same time that one sets out from the English capital for Edinburgh at 8 mph. Where will the couriers meet?

A company dining together find that the bill amounts to $175. Two were not allowed to pay. The rest found that their shares amounted to $10 per person more than if all had paid. How many were in the company?

- Show that an “Euler path” over a series of bridges connecting certain regions (a path that crosses each bridge exactly once) is always possible if there are either two or no regions that are approached by an odd number of bridges.

- *Find the numbers of vertices, edges, and faces for each of the five regular polyhedral and confirm that Euler’s formula holds in these five cases.

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