1 Carl has a trick die. The probabilities of rolling 1, 2, 3, 4, 5, or 6 are shown below. Roll 1 2 3 4 5 6 Probability 0.1 0 0.6 0.1 0.1 0.1 For one roll of the die, let D = {roll is even}, E = {roll is 1, 2, or 3}, F = {roll is 7}.
Find the following
probabilities. P(D) = Answer P(DC) = Answer P(E) = Answer P(EC) = Answer P(F) = Answer P(FC) =
probabilities. P(D) = Answer P(DC) = Answer P(E) = Answer P(EC) = Answer P(F) = Answer P(FC) =
Answer 2-Here are the counts of the student body at a college, broken down by age and gender. Suppose a student is chosen at random from this population. Age 14-17
18-24 25-34 35 or older Male 80 1450 600 200 Female 20 1550 650 450 Find the following probabilities. Answer using decimal values (not fractions), and round to three places after the decimal when necessary. What is the probability that the student is female?
Answer What is the conditional probability that the student is female given that the student is at least 35 years old? Answer What is the probability that the student is female or is at least 35 years old? (Recall that in Math and Statistics, we always use “or” in the inclusive sense.) Answer What is the probability that the student is female and is at least 35 years old?
18-24 25-34 35 or older Male 80 1450 600 200 Female 20 1550 650 450 Find the following probabilities. Answer using decimal values (not fractions), and round to three places after the decimal when necessary. What is the probability that the student is female?
Answer What is the conditional probability that the student is female given that the student is at least 35 years old? Answer What is the probability that the student is female or is at least 35 years old? (Recall that in Math and Statistics, we always use “or” in the inclusive sense.) Answer What is the probability that the student is female and is at least 35 years old?
Answer 3-A small high school has sixty students in the senior class. There are twenty total seniors who compete in the school rodeo, some of whom are also in the band. There are fifteen total seniors who play in the school band, some of whom also participate in the rodeo. In fact, there are exactly five students who are in both the band and the rodeo. Part (a): Fill in the values for the following frequency table: In the band Not in the band Totals Participates in rodeo Answer Answer Answer Not in rodeo Answer Answer Answer Totals Answer Answer Answer Part (b): One student is to be selected at random from the sixty seniors. Let R represent the event that this student competes in the rodeo. Let B represent the event that the student plays in the school band. Answer using decimal values (not fractions), and round to three places after the decimal when necessary. P(R) = Answer P(B) = Answer P(R and B) =
Answer P(R or B) = Answer P(R|B) =
Answer P(R or B) = Answer P(R|B) =
Answer 4-Are events R and B disjoint (mutually exclusive) for this senior class (yes/no)? Provide a mathematical explanation for your answer using one or more probabilities.
5-Are events R and B independent for this senior class (yes/no)? Provide a mathematical explanation for your answer using one or more probabilities.
6-An “unfair” coin is flipped numerous times, and it is determined that heads appears 4 times for every time tails appears. Find the following probabilities.
Answer using decimal values (not fractions), and round to two places after the decimal if necessary.
Answer using decimal values (not fractions), and round to two places after the decimal if necessary.
(a) What is the probability a single coin flip comes up heads?
Answer (b) If the coin is flipped twice in a row, what is the probability both will come up
heads? Answer (c) If the coin is flipped twice in a row, what is the probability both will come up tails? Answer (d) If the coin is flipped twice in a row, what is the probability of getting heads once and tails once (in either order)?
heads? Answer (c) If the coin is flipped twice in a row, what is the probability both will come up tails? Answer (d) If the coin is flipped twice in a row, what is the probability of getting heads once and tails once (in either order)?
7 Consider two independent events A and B, P(A) = 0.4 and P(B) = 0.5. Answer using decimal values (not fractions). P(A and B) = Answer P(A or B) = Answer P(AC) = Answer P(AC and B) = Answer 8-A certain genetic abnormality is present in 3% of all mice. There is a test geneticists use to check for this abnormality, but the test does not always give the right answer. When the abnormality is present in a mouse, the test correctly identifies its presence in 95% of the time. When the abnormality is not present, the test correctly shows this 90% of the time. Suppose a mouse is chosen at random. G = the event that a randomly selected mouse actually has the genetic abnormality. T = the event that the test shows the presence of the abnormality. Part a: Complete the following table for a hypothetical population of 10,000 mice. Test shows abnormality is present Test shows abnormality is not present Total Actually has abnormality Answer Answer Answer Does not have abnormality Answer Answer Answer Total Answer Answer 10000 Part (b): Find the following probabilities.
Answer using decimal values (not fractions), and round to four places after the decimal when necessary. P(G) = Answer P(T|G) = Answer P(T) = Answer P(G|T) = Answer 9-Write a sentence or two explaining, in non-technical language, what your answer for P(G|T)
Answer using decimal values (not fractions), and round to four places after the decimal when necessary. P(G) = Answer P(T|G) = Answer P(T) = Answer P(G|T) = Answer 9-Write a sentence or two explaining, in non-technical language, what your answer for P(G|T)
