When the probability of event B is affected by the occurrence of event A, the events are not independent. Let P(B | A) denote the probability of B given the condition that A has occurred. This is called a conditional probability.
When the probability of event B is affected by the occurrence of event A, the events are not independent. Let P(B | A) denote the probability of B given the condition that A has occurred. This is called a conditional probability.
Type | by holding down Shift and type
For independent events A and B, P(B | A) = P(B), and P(A | B) = P(A)
For dependent events A and B
P(B | A) ≠ P(B). The occurrence of A has changed the probability of B.
P(A | B) ≠ P(A). The occurrence of B has changed the probability of A.
For dependent events, P(A and B) = P(A) x P(B | A) = P(B) x P(A | B). This is the General Multiplication Rule.
Assume the following joint and marginal probabilities:
When we know the condition that some event has occurred, the table reduces to a row or column matching the condition. For example, when we know that the party is Democrat, the table reduces to the Democrat column:
P(Yes | Democrat) is the probability of event Yes given the condition that the event Democrat has occurred. In condition Democrat, Yes occurs at a rate of 0.15 in 0.40. So P(Yes | Democrat) = 0.15/0.40 = 0.375.
Supplemental
Course Content Session 3 Lecture beginning p. 13
Additional Reading
Video
P(Male | Republican) is a ________ probability.
Joint
Marginal
Conditional
Question 2Given the following partial relative frequency table
Republican Democrat Independent
Male 0.194 0.182 0.130
Female 0.193 0.150 ?
Compute P(Female | Democrat), and enter your answer with 3 decimal places.
Question 3Given the following partial relative frequency table
Republican Democrat Independent
Male 0.134 0.108 0.142
Female 0.132 0.144 ?
Compute P(Republican | Male), and enter your answer with 3 decimal places.
Question 4Assume breast cancer affects 0.008 of the female population between 45 and 55 years of age.
There are two kinds of positive test results:
True positive (the test indicates you have a disease, and you actually have it)
False positive (the test indicates you have a disease, but you actually do not).
Assume mammograms are
0.93 accurate detecting people who actually have breast cancer (true positive rate)
0.91 accurate for people who do not have breast cancer (true negative rate).
Compute the probability that a female between the ages of 45 and 55 who tests positive for breast cancer has breast cancer, and enter your answer with 3 decimal places.
Answer:
0.097 Incorrect Response (0.077)
Question 5Misa earned a score of 81 on her latest exam. The professor determined that all of the scores from this exam had a normal distribution with a mean of 89 and a standard deviation of 1.
What is Misa’s Z score on her exam?
Round to three decimal digits.
Question 6Blue Crab lengths have a normal distribution with a mean of 3 inches and a standard deviation of 2 inches.
What is the Z value of 7 inches?
Round to three decimal digits.
Question 7In every normal distribution
The mean = 0 and the standard deviation = 1
The mean is larger than the standard deviation
The interquartile range covers 68% of the values
The mean and the median are equal
Question 8In a normal distribution the probability of a value larger than one standard deviation above the mean is:
32%
16%
68%
There is not enough information to answer the question
Question 9In a normal distribution the probability of a value between 2 and 3 standard deviations below the mean is:
2.35%
.15%
-2.35%
-.15%
Question 10The Standard Normal Distribution is a Normal Distribution with the following characteristics:
The mean is 1 and the standard deviation is 0
The mean is 0 and the standard deviation is 1
The mean and the standard deviation are 0
The mean and the standard deviation are 1
Question 11Choose all of the correct answers for the characteristics of a Binomial Probability Distribution.
An example of a binomial trial is rolling a die.
Each binomial trial has only 2 possibilities.
The binomial trials are independent of each other.
The variables are continuous.
An example of a binomial trial is flipping coins.
The binomial trials are dependent on each other.
There can be three or more outcomes of each binomial trial.
The variables are discrete.
Question 12Select all correct answers for the Poisson probability distribution.
The Poisson distribution’s mean=median=mode.
An example of a Poisson trial is counting the number of misspelled words in a magazine article.
An example of a Poisson trial is selecting the members of a committee from one business.
The Poisson distribution describes the number of events occurring in a unit of space or time.
The Poisson distribution is always positively skewed.
The Poisson distribution describes a situation where the probability of success does not remain the same from trial to trial.
The variables in a Poisson trial are measured.
The variables in a Poisson trial are counted.
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