Advanced Precalculus Advanced Precalculus Notes 12.3 Probability

Probability model: 1. Sample space: set whose elements represent all the possible outcomes of an experiment. 2. The measure of how likely it is that some event will occur; a number expressing the ratio of favorable cases to the whole number of cases possible.

In a bag of M&Ms, the candies are red, green, blue, brown, yellow, and orange. Therefore, the sample space is: { red, green, blue, brown, yellow, orange} Which of the following are probability models: OutcomeProbability Red.3 Green.15 Blue0 Brown.15 Yellow.2 orange.2 OutcomeProbability Red.3 Green-.3 Blue.2 Brown.4 Yellow.2 orange.2 OutcomeProbability Red0 Green0 Blue0 Brown0 Yellow1 orange0 OutcomeProbability Red.1 Green.1 Blue.1 Brown.4 Yellow.2 orange.3

An experiment consists of a rolling a fair die once. Construct a probability model for this experiment. a) List the sample space. b) List the probability of each outcome. c) Find the probability of each outcome if only 3 or 4 could occur and 4 is twice as likely as 3.

An experiment consists of tossing a coin. The coin is weighted so that heads (H) is three times as likely to occur as tails (T). Construct a probability model for this experiment. a)List the sample space. b) List the probability of each outcome. P(E) = Number of ways that E can occur Number of all logical possibilities

Calculate the probability that in a 3-child family there are 2 boys and 1 girl. Assume equally likely outcomes. Consider the experiment of rolling a single fair die. Let E represent the event “roll an odd number,” and let F represent the event “roll a 1 or 2.” a) Write the even E and F.b) Write the event E or F. c) Compute P(E) and P(F).d) Compute e) Compute

Addition Rule: = If P(E) = 0.2, P(F) = 0.3, and = 0.1, find the probability of E or B. ie:

Mutually Exclusive Events: If P(E) = 0.4, and P(F) = 0.25, and E and F are mutually exclusive, find

Computing Probabilities of Complementary Events: On the local news the weather reporter stated that the probability of rain tomorrow is 40%. What is the probability that it will not rain? What is the probability that in a group of 10 people at least 2 people have the same birthday? Assume that there are 365 days in a year.

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