A box contains 4 red markers and 2 blue markers
Question # 00489448
Posted By:
Updated on: 02/23/2017 05:40 AM Due on: 02/23/2017
Name:
Please work all problems and show your work. Remember, an answer with no justification is no answer.
Based on concepts from Section 4.3 (More Conditional Probability – Use Trees AND Conditional Probability Formula
for each problem)
1) A box contains 4 red markers and 2 blue markers. A marker is selected at random and its color is noted. If it is red it
is replaced; otherwise it is not. A second marker is selected and its color is noted. If the second is blue, find the
probability that the first was blue?
Please work all problems and show your work. Remember, an answer with no justification is no answer.
Based on concepts from Section 4.3 (More Conditional Probability – Use Trees AND Conditional Probability Formula
for each problem)
1) A box contains 4 red markers and 2 blue markers. A marker is selected at random and its color is noted. If it is red it
is replaced; otherwise it is not. A second marker is selected and its color is noted. If the second is blue, find the
probability that the first was blue?
2) It is believed that 8% of the population has hepatitis. A medical firm has a new test to detect hepatitis. It was found
that if a person has hepatitis, the test will detect it (show a positive result) in 96% of the cases; it was also found
that it will still show a positive result in 3% of those who do not have hepatitis. What is the probability that a
person who tests positive actually has hepatitis?
that if a person has hepatitis, the test will detect it (show a positive result) in 96% of the cases; it was also found
that it will still show a positive result in 3% of those who do not have hepatitis. What is the probability that a
person who tests positive actually has hepatitis?
3) An unfair coin with Pr[H] = 0.55 is flipped. If the flip results in a head, one student is selected at random from a class
of 4 girls and 6 boys. If the flip results in a tail, one student is selected from a different class containing 3 girls and
7 boys. Find the probability that the flip resulted in tails given that a boy was selected.
of 4 girls and 6 boys. If the flip results in a tail, one student is selected from a different class containing 3 girls and
7 boys. Find the probability that the flip resulted in tails given that a boy was selected.
4) At a state university, 60% are undergraduates, 35% graduates and 5% are in special program. Also, 20% of the
undergraduates, 40% of the graduates, and 70% of the special program students are local residents. If a student is
selected at random and found to be a resident, find the probability that this student is not a graduate student.
undergraduates, 40% of the graduates, and 70% of the special program students are local residents. If a student is
selected at random and found to be a resident, find the probability that this student is not a graduate student.
5) Statistics shows that 6% of men are colorblind and 0.4% of women are colorblind. Assume that the population is
half male and half female. Find the probability that the person selected is male given that they are colorblind?
half male and half female. Find the probability that the person selected is male given that they are colorblind?
6) At a small college, 60% of the students are women and women are twice as likely to take aerobics class. In one
semester, 30% of women took the class. If a randomly selected student is found to have taken the aerobics class,
what is the probability that this student is a woman?
semester, 30% of women took the class. If a randomly selected student is found to have taken the aerobics class,
what is the probability that this student is a woman?
7) One-half of the students on campus are females. Females are three times as likely to enjoy romantic comedies as
men. Assume 60% of the women on campus enjoy romantic comedies. If a student is selected at random and is
found to enjoy romantic comedies, what is the probability the student is a male?
men. Assume 60% of the women on campus enjoy romantic comedies. If a student is selected at random and is
found to enjoy romantic comedies, what is the probability the student is a male?
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Rating:
/5
Solution: A box contains 4 red markers and 2 blue markers