7.6 Using Probability

The following examples will explore more applications of probability. Let us start by looking at flipping a coin, which is a single event. The total number of possible outcomes when flipping a coin is 2, either heads or tails. The two would be placed in the denominator. If we wanted to know the probability that the outcome would be heads then the expression would look like images or a 0.5% chance it would be heads.

Frequently, we want to know the probability of two things happening; in other words, one thing happens AND then another thing happens (AND means multiply). You multiply the probability of one thing happening by the probability of the other thing happening. What is the probability of the following:

1. Flipping two heads in a row? [Answer: images].
2. Flipping three heads in a row? [Answer: images].
3. Flipping six heads in a row? [Answer images] (rolling one die twice is the same as rolling two dice together once).
4. Drawing 2 aces? It depends on if you put the first one back before drawing the second. If you did put it back then it is 4/52 × 4/52 = 16/2704 or 1/169. If you ...

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