Probability
1. Who is George W. Bush's favorite
a. Chandler b. Joey c. Monica d. Pheobe e. Rachael f. Ross 2. How many cousins does Professor DeMaio have? a. 1 b. 2 c. 3 d. 4 e. 5 For both questions random guessing must be employed. The probability of a correct answer in question number 1 is 1/6 or about 16.67%. The probability of a correct answer in question number 2 is 1/5 or 20%. This concept of counting and dividing is
The process of making an observation or taking a measurement of one or more experimental units is called an example: An experiment consists of randomly picking a card from a A - The 8§ is selected. B - A red card is selected. C - The J© is not selected.
example: An experiment consists of watching ten different movies made after 1982
The , is a number between 0 and 1 that measures the likelihood that event P(A)A will occur when the experiment is performed. If P(A) is 0 then A is guaranteed not to occur. If P(A) is 1 then A is guaranteed to occur.
Two events example: Let an experiment consist of rolling a pair of fair dice.
Are events Are events Are events
Let an experiment consist of a collection of . example: An experiment consist of flipping a fair coin twice. Compute the probabilities of the following events.
The first step is to construct the sample space. In this case the sample space is as follows.
example: A pair of fair dice are rolled. Compute the probabilities of the following events.
Once again, the first step is to construct the sample space.
Homework Section 3-2: 2-5, 7, 9, 10, 13, 15, 17, 20, 28
If
example: The probability that John makes a B in Math 1107 is 35%. These events are clearly mutually exclusive and the
example: A fair coin is flipped twice.
It is always true that P(A or B) = P(A) + P(B) - P(A and B).
The complement of an event example: A fair coin is flipped twice. Describe . Compute
example: A pair of fair dice are rolled. Let Describe . Compute
Fact: P(A) + P(
) = 1. This fact quickly implies that
Homework Section 3-3: 1, 3, 4, 7-20, 25, 26 Consider the experiment of randomly picking a card from a standard A - The suit § is selected. B - The rank King is selected. Compute
P(A and B)
P(A or B)
P(A and B)
P(A and B)
On the first day of spring training you are asked,
Halfway through the year when the Braves have won
At the end of the regular season, the Braves have clinched a playoff birth,
The Braves have a 3-0 games lead and are up 15-0 at the
Why do your answers change? You are repeatedly asked the same question. The probability of event .P(A|B)
example: A pair of dice are thrown one at a time. Let
i. What is the probability the sum of the dice is 9? ii. What is the probability the sum of the dice is 9, given that the first
Can I use conditional
probability to make money playing blackjack?
If
example: The probability that on any given morning 85 south near the connector
.35*.57 = .1995
An box contains 3 white balls, 4 red balls and 5 black balls.
An box contains 3 white balls, 4 red balls and 5 black balls. In this case, selections of the balls are not independent events.
It is always true that P(A and B) = P(A) * P(B|A). An box contains 3 white balls, 4 red balls and 5 black balls.
If a sample size is no more than 5% of the size of the population,
The defect rate for manufacturing
a cd is 2%. If a particular store
Homework Section 3-4: 1-4, 8, 9, 12, 13, 17, 19, 20, 25, 26, 27
The event of "at least one" is equivalent to "one or more."
Note that if event
A die is independently rolled 5 times. What is the
According to Nielson Media Research, 30% of all televisions are tuned to Assuming that this show is being broadcast and that the televisions are randomly selected, find the probability that at least 1 of 15 televisions is tuned to . NFL Monday Night Football
Homework Section 3-5: 1-4, 7-10, 15, 17, 23
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