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# Pre-Cal 40S Slides May 21, 2008

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Introduction to probability & sample spaces.

Introduction to probability & sample spaces.

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• 1. What is the probability that the sky will fall? Write your answer as a fraction. Do not discuss with a neighbour. An Introduction to Probability http://mathforum.org/dr.math/faq/faq.prob.intro.html Chicken Little by ﬂickr user damonj74
• 2. Some vocabulary ... Probability: the branch of mathematics that deals with chance. Sample Space (Ω): the set of all possible outcomes for a given quot;Experimentquot; represented by capital omega Ω. Event (E): A subset of the sample space. A particular occurance in a given experiment. Simple Event: The result of an experiment that is carried out in a single step. Example: Flip a coin. The result is heads (a simple event) Compound Event: The result of an experiment carried out in two (or more) steps. Example 1: Flip a coin and roll a die - 6 .The result is {H,6} Example 2: Flip a coin twice. The result is {H,T}
• 3. Calculating the Probability of Event A number of favourable outcomes sample space Probability can be expressed as: - a Ratio - a Fraction IMPORTANT: Probability of any event - a Decimal is always a number between 0 and 1. - a Percent
• 4. Certain Event: an event whose probability is 1 Example: roll a die - 6 and get a result less than 10 Impossible Event: an event whose probability is 0. Example: roll a die - 6 and get a 7 Complimentary Event: the compliment of E is E': If P(E) = a then P(E') = 1-a Example: Given a standard deck of cards, a card is drawn at random. P(spade) = (13/52) = (1/4) P (not a spade) = 1 - (1/4) = (3/4)
• 5. Determine the sample space when a fair die is rolled once. Solution: It is possible to roll a 1, 2, 3, 4, 5 or 6. This is the sample space. {1, 2, 3, 4, 5, 6} Determine the sample space for rolling a six sided die and ﬂipping a coin.
• 6. Determine the probability of rolling a 2 when rolling a fair die. Determine the probability of getting a head and an odd number when rolling a die and ﬂipping a coin.
• 7. A coin is ﬂipped three times. Draw a tree diagram to illustrate the sample space.
• 8. A fair six-sided die is rolled twice. Draw a chart to illustrate the sample space.
• 9. A bus is scheduled to arrive at a train station at any time between 07:05 and 07:15 inclusive. A train is scheduled to arrive between 07:11 and 07:17 inclusive. The arrival of a bus at 7:06 and a train at 07:14 can be represented by the ordered pair (6, 14). Times are expressed in whole minutes. a) Sketch a sample space for this event (use a chart). b) How many ordered pairs are there in this sample space? c) How many ordered pairs have the bus and the train arriving at the same time? d) How many ordered pairs have the train arriving after the bus? e) What is the probability of the bus arriving after the train?