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29-Jun-17
Probability (1)
I.
Identify each of the following as to the most likely way that the probability was determined.
A) theoretically
B) empirically (observed relative frequency)
C) subjectively (personal)
____
1.
The probability that a sixty year old man lives one more year is 0.935.
____
2.
The probability that red appears on a spin of a roulette wheel is 9/19.
____
3.
The probability that a patient experiences side effects from a vaccination is 0.004.
____
4.
The probability that the S.F. Giants win the National League West is 0.40.
____
5.
The probability of being dealt a royal flush in poker is approximately 0.00000154.
____
6.
The probability that Flight 132 from JFK to SFO is on time tomorrow is 0.63.
____
7.
The probability that a randomly selected card from a deck is a heart is ¼.
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8.
The probability that a house in Fairfield suffers fire damage next year is 0.008.
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9.
The probability that a seven is rolled on a pair of dice is 1/6.
____
10.
II.
The probability of rain in the next two weeks is 0.30.
An experiment consists of two steps: first flipping two coins and then if the coins both land heads up a die
is rolled otherwise a coin flipped. (Outcomes are listed like HH3 or THH.)
1.
Make a tree diagram and write out (using proper set notation) the sample space for this experiment.
2.
Write out (using proper set notation) the event that exactly two tails appear.
3.
Write out (using proper set notation) the event that an odd number is rolled on the die.
III.
IV.
Let P(A) = 0.7, P(B) = 0.5 and P(A and B) = 0.3, use the rules of probability to find each of the following:
c
______
5.
P(B | A).
______
P(B )
c
______
6.
P(A and B)
c
______
3.
P(A or B)
______
7.
P(A or B)
c
______
4.
P(A | B)
______
8.
P((A or B) )
1.
P(A )
2.
c
______
A recent poll of voters on the ERA (Equal Rights Amendment) produced the results in the table below:
Male
Female
For
100
210
310
Against
100
90
190
200
300
500
Assuming that one of these voters is selected at random find:
1.
P(male)
______
2.
P(male for the ERA)
______
3.
P(male | for the ERA)
______
4.
P(for the ERA | male)
______
5.
Use the above probabilities to show that gender and being for the ERA are not independent.