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M119L09to10 - (Lesson 9 Probability Basics 4-2 4.01 CHAPTER...

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(Lesson 9: Probability Basics; 4-2) 4.01 CHAPTER 4: PROBABILITY The French mathematician Laplace once claimed that probability theory is nothing but “common sense reduced to calculation.” This is true many times, but not always …. LESSON 9: PROBABILITY BASICS (SECTION 4-2) PART A: PROBABILITIES Let P A ( ) = the probability of event A occurring. P A ( ) must be a real number between 0 and 1, inclusive: 0 P A ( ) 1 Scale for P A ( ) : 1 P A ( ) = the probability of event A not occurring, P not A ( ) . Note: The event “not A ” is also called the complement of A , denoted by A or A C . Example 1: If the probability that it will rain here tomorrow is 0.3, then the probability that it will not rain here tomorrow is 1 0.3 = 0.7 .
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(Lesson 9: Probability Basics; 4-2) 4.02 PART B: ROUNDING Rounding conventions may be inconsistent. Triola suggests either writing probabilities exactly, such as 1 3 , or rounding off to three significant digits, such as 0.333 (33.3%) or 0.00703 (0.703%). Although there is some controversy about the use of percents as probabilities, we will sometimes use percents. Remember that “leading zeros” don’t count when counting significant digits. It is true that 0.00703 has five decimal places. If your final answers are rounded off to, say, three significant digits, then intermediate results should be either exact or rounded off to more significant digits (at least twice as many, six, perhaps). Note: If a probability is close to 1, such as 0.9999987, or if it is close to another probability in a given problem, then you may want to use more than three significant digits. Always read any instructions in class. PART C: THREE APPROACHES TO PROBABILITY Approach 1): Classical Approach Assume that a trial (such as rolling a die, flipping a fair coin, etc.) must result in exactly one of N equally likely outcomes (we’ll say “elos”) that are simple events, which can’t really be broken down further. The elos make up the sample space, S .
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