1. P( 2. P(S) = 1 *The largest possible probability is of a certain event (event equal to S, the sample space 3. 0 **If you ever get a negative probability or a probability greater than 1, recheck you work and find your mistake. Mutually exclusive events: Two events that cannot both occur at the same time. i.e. E
A Pair of dice is rolled. Notice that
sample space is The sample space is all possible outcomes of two dice rolled. Sample space has 36 elements. (see page 137) Find the probability that: a) the sum is less than 5 b) the sum is odd c) the sum is less than 9 and odd. d) The sum is less than 9 or odd a) P(a) = n(a)/n(S) = 6/36 = 1/6 b) P(b) = 18/36 = ½ c) P(c) = 12/36 = 1/3 d) Use complement: the sum is greater than 9 and even = 4/36 = 1/9. So 1 – 1/9 = 8/9 Notice all of the probabilities occur between 0 and 1.
4.
P(E 5. If E and F are mutually exclusive: P(E 6. P(E) + P(E’) = 1 or 1 – P(E) = P(E’) or 1 – P(E’) = P(E) Example 2: Find the odds from EX 1. a) n(a) : n(a’) = 6 : 30 = 1 : 5 b) n(b) : n(b’) = 18 : 18 = 1 : 1 c) n(c) : n(c’) = 12 : 24 = 1 : 2 d) n(d) : n(d’) = 32 : 4 = 8 : 1 #59 requires a lot of thought. Use the Rules of Probability!
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