By William Feller

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**Extra info for An introduction to probability theory and its applications**

**Example text**

Recall that such a set of events is referred to as a partition. 11) The latter result is referred to as the principle of total probability and is frequently used in solving problems. 11) is illustrated by a Venn diagram in Fig. 4. The event B is comprised of all of the pieces that represent intersections or overlap of event B with the events Ai. 4 Venn diagram illustrating the principle of total probability. Let us consider the following example to illustrate the formulas in this section. 1: Simon’s Surplus Warehouse has large barrels of mixed electronic components (parts) that you can buy by the handful or by the pound.

A) Draw the tree diagram and the sample space for this experiment. (b) Given that the first bit is a zero, what is the probability of more zeros than ones? (c) Given that the first two bits are 10, what is the probability of more zeros than ones? (d) Given that there are more zeros than ones, what is the probability that the first bit is a zero? 4. 9. 2. What is the probability that Beetle will be late for his date? 31 Rudy is an astronaut and the engineer for Project Pluto. Rudy has determined that the mission’s success or failure depends on only three major systems.

2). The result of two good diskettes is represented by the events A4, A6, and A7. 1). That is, Finally, a single good diskette is represented by the events A2, A3, and A5. By an identical procedure it is found that this result also occurs with probability □ To be sure you understand the steps in this example, you should repeat this example for the case where the probability of selecting a good diskette is increased to . In this case the probability of all of the events Ai are not equal. 2 Problems involving counting Many important problems involve adding up the probabilities of a number of equallylikely events.