Basic Terms of Probability课件.ppt

Basic Terms of Probability Section 3.2 精品文档 Definitions Experiment: A process by which an observation or outcome is obtained. Sample Space: The set S of all possible outcomes of an experiment. Event: Any subset E of the sample space S. 精品文档 Probability of an Event Probability of an event is a measure of the likelihood that the event will occur. Remember probability is a number not a set. Mathematically speaking the probability of an event E denoted by P(E) is: P(E) = n(E)/n(S). Recall that that n(E) is the cardinal number of set E and n(S) is the cardinal number of set S. 精品文档 Odds of an event Don’t confuse probability with odds. Every state lottery supposedly tells you the odds of winning. It turns out they don’t. They tell you the probability of winning. By definition, the odds of event E happening are denoted by o(E), which is given by: o(E) = n(E):n(E’). In words this says, that the odds of event E happening are number of times E happens divided by the number of times E does not happen. Think success compared with failure. Note odds use : , think of this as a fraction symbol or division sign. 精品文档 NJ state Lottery According to the New Jersey state lottery, the odds of winning the Pick – 6 Jackpot is 1:13,983,816. However this is not correct. What they tell you is the probability. Remember the number of Pick – 6 numbers is 49C6 . This number equals 13,983,816. The sample space contains 13,983,816 numbers and the winning number is just one of these. Hence a probability. The correct way to state the odds would be 1:13,983,815. There is 1 successful number and 13,983,815 unsuccessful number. 精品文档 Relative frequency Tossing a single coin has a sample space of Heads and Tails. That is S={H,T}. Theoretically speaking the probability of tossing a head is ?. Let say you flip a coin 10 times and record the result of each toss. According to my results I recorded seven trials with heads. This would yield a relative frequency 7/10 or 0.7. We call this t