# Human Nature, Biology, and Social Structure: A Critical Look at WhatScience Can Tell Us About Society

## An Introduction to Mathematical Probability

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## Dependent Events

The probability that two dependent events will happen may be expressed as follows: If pl is the probability that event X will happen and, after X has happened, p2 is the probability that event Y will happen, then the probability that the events will occur in the order X,Y is p1p2, the product of their respective probabilities.

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Exercises:
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- 1.) A bag contains five green marbles, four yellow marbles, and nine white marbles. If two marbles are drawn in succession, and the first marble is not replaced before the second is drawn, what is the probability that:
- ____ a.) the second marble is yellow, if the first marble drawn is green?
- ____ b.) the second marble is white, if the first marble drawn is yellow?
- ____ c.) both marbles are green?
- ____ d.) both marbles are yellow?
- ____ e.) both marbles are white?
- 2.) A boX contains ten slips of paper. Three slips are marked with the letter G, two slips are marked M, and five slips are marked K. If two slips of paper are drawn in succession, and the first is not replaced before the second is drawn, what is the probability that:
- ____ a.) the first slip is marked G, and the second is marked K?
- ____ b.) the first slip is marked G, and the second is marked H?
- ____ c.) the first is marked H, and the second is marked G?
- ____ d.) the first is marked K, and the second is marked G?
- ____ e.) the first is marked H, and the second is marked K?
- ____ f.) the first slip is marked K, and the second slip is marked M?
- ____ g.) both slips are marked G?
- ____ h.) both slips are marked M?
- ____ i.) both slips are marked K?
- 3.) The probability that Mr. Smith will be elected president is 5/7, and if he is elected, the probability that he will appoint Mr. Jones attorney general is 2/3. Find the probability that Mr. Jones will be attorney general.