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Math 242 Chapter 4/Section 1- Topics: Probability Basics and Rules of Probability Define the following terms:
- Probability for Equally Likely Outcomes (f/N Rule)
- Experiment
- Event
- Sample Space
- State the 3 basic properties of probabilities
- Mutually Exclusive Events
- State the rule for P(A or B)
- State the Complementation Rule Math 242
Solve the following problems:
- Which of the following numbers could not possibly be a probability? Justify your answer. a. 3/4 b. 1.2 c. 0 d. 1 e. 5/4 f. 0.
- An experiment has 50 possible outcomes, all equally likely. An event can occur in 3 ways. What is the probably that the event occurs?
- Given a standard playing cards, find the following probability. a. Getting an ace b. Getting a heart c. Getting an ace and a heart d. Getting an ace or a heart
- Flipping a coin 3 times, find the following probability. a. Exactly 2 heads Math 242
- Rolling a dice twice, find the following probability a. 6 does not appear b. At least one 6 c. The sum is greater than 10 d. The sum is less than or equal to 10
- Suppose that A and B are mutually exclusive events such that P(A)=0.3 and P(B)=0.4. Determine P(A or B).
- Suppose that A and B are events such that P(A) = 1/5, P(A or B) = 1/3 and P(A & B) = 1/10. a. Find P(B) b. Are events A and B mutually exclusive? Justify your answer. Math 242
Math 242 Chapter 4/Section 1- Topics: Probability Basics and Rules of Probability Define the following terms:
- Probability for Equally Likely Outcomes (f/N Rule) Suppose an experiment has N possible outcomes, all equally likely. An event that can occur in f ways has probability of occurring. In other words, probability of an event = where f represents number of ways event can occur and N represents total number of possible outcomes.
- Experiment An action whose outcome cannot be predicted with certainty.
- Event The collection of all possible outcomes for an experiment.
- Sample Space A collection of outcomes for the experiment. Any subset of the sample space.
- State the 3 basic properties of probabilities Property 1: The probability of an event is always between 0 and 1 Property 2: The probability of an event that cannot occur is 0 Property 3: The probability of an event that must occur is 1
- Mutually Exclusive Events Two or more events are mutually exclusive if no two of them have outcomes in common. In other words P(A and B) = 0 if A and B are mutually exclusive.
- State the rule for P(A or B) , if A and B are mutually exclusive, then .
- State the Complementation Rule For any event E,. f N f N P ( AorB ) = P ( A ) + P ( B ) − P ( A a n d B ) P ( AorB ) = P ( A ) + P ( B ) P ( E ) = 1 − P ( n ot E ) Math 242
b. At least 2 heads From part a, there are 8 outcomes with the event at least 2 heads occurring 4 times (THH, HHT, HTH, HHH), Therefore P(At least 2 heads) = 4/8 = 1/ c. All 3 heads From part a, there are 8 outcomes with the event all 3 heads occurring 1 time. Therefore P(All 3 heads) = 1/
- Construct a Venn diagram representing the following event a. A & B b. A or B c. A and B and not C d. (Not A) & B Math 242
- Rolling a dice twice, find the following probability a. 6 does not appear There are 36 total outcomes. Since 6 appears 11 times (1-6, 2-6, 3-6, 4-6, 5-6, 6-6, 6-5, 6-4, 6-3, 6-2, 6-1), P( 6 appears) = 11/36. Therefore by complementation rule P(6 does not appear) = 1-11/36 = 25/ b. At least one 6 From part a, P(at least one 6) = 11/36. c. The sum is greater than 10 First notice that the largest sum possible is 12 (6+6) so we’re finding the probability of sum is either 11 or 12. Therefore there are 3 ways to get the sum that is greater than 10 (5-6, 6-5, 6-6). Therefore P(Sum is greater than 10) = 3/36 = 1/ d. The sum is less than or equal to 10 By part c, using the complementation rule P(Sum is less than or equal to 10) = 1 - P(Sum > 10) = 1 - 1/12 = 11/
- Suppose that A and B are mutually exclusive events such that P(A)=0.3 and P(B)=0.4. Determine P(A or B). P(A or B) = P(A) + P(B) since A and B are mutually exclusive. Therefore P(A or B) = 0.3 + 0. = 0.
- Suppose that A and B are events such that P(A) = 1/5, P(A or B) = 1/3 and P(A & B) = 1/10. a. Find P(B) P(A or B) = P(A) + P(B) - P(A and B). Therefore b. Are events A and B mutually exclusive? Justify your answer. No, A and B are not mutually exclusive since P(A and B) does not equal to 0. 1 3 = 1 5 + P ( B ) − 1 10 P ( B ) = 1 3 − 1 5 + 1 10 = 7 30 Math 242
