Question
In: Statistics and Probability
1. Assume that you have applied for two scholarships, a Leadership scholarship (denoted by L) and...
1. Assume that you have applied for two scholarships, a Leadership scholarship (denoted by L) and a Merit scholarship (denoted by M). The probability that you receive a Leadership scholarship is 0.25. The probability of receiving both scholarships is 0.15. The probability of receiving at least one of the scholarships is 0.45.
Write the probability statement using the events defined in the problem, e.g., P(L), P(M). Then compute the probability. Use 4-decimal accuracy when necessary. Please show steps.
a) [3 points] The probability that you will receive a Merit scholarship is: P(__________) = __________. Show detailed steps below.
b) [3 points] Events L and M __________ (Choose one: are, are not) mutually exclusive. Why or why not? Explain below.
c) [3 points] Events L and M __________ (Choose one: are, are not) independent. Why or why not? Explain below.
d) [3 points] The probability of receiving the Leadership scholarship given that you have been awarded the Merit scholarship is P(__________) = __________. Show detailed steps below.
e) [3 points] The probability of receiving the Merit scholarship given that you have been awarded the Leadership scholarship is: P(__________) = __________. Show detailed steps below.
Solutions
orchestra answered 1 year agoRelated Solutions
Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A)....
Assume you have applied for two
scholarships, a Merit scholarship (M) and an Athletic scholarship
(A). The probability that you receive an Athletic scholarship is
0.18. The probability of receiving both scholarships is 0.11. The
probability of getting at least one of the scholarships is 0.3.
a.
What is the probability that you
will receive a Merit scholarship? Hint:
P(M∪A) = P(M) + P(A) – P(M∩B)
b.
Are events A and M mutually
exclusive? Why or why not? Explain.
c....
Linda Grabeck did not have an athletic scholarship, there simply weren't enough scholarships to go around....
Linda Grabeck did not have an athletic scholarship,
there simply weren't enough scholarships to go around. Until the
NCAA relaxed the rules and allowed you to come up with more
scholarships, that was the way it had to be.
When you spoke to Linda about your concerns, she was
very open about her part-time job. She indicated that, of course,
college was very expensive. Tuition and fees were high and the cost
of books and other materials grew more expensive...
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disbursements of $2,500 per scholarship coming on year from now.
The endowment earns a 6% annual interest. If the scholarships are
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B) Events (accepted by school C) and (accepted by school D) are
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Question 1 Suppose we have two goods, whose quantities are denoted by A and B, each...
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4.
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Assume you are considering a portfolio containing two assets, L and M. Asset L will represent...
Assume you are considering a portfolio containing two assets, L
and M. Asset L will represent 39% of the dollar value of the
portfolio, and asset M will account for the other 61%. The
projected returns over the next 6 years, 2018-2023, for each of
these assets are summarized in the following table:
Projected Return
Year Asset L Asset M
2018 13% 21%
2019 13% 17%
2020 15% 17%
2021 17% 14%
2022 17% 12%
2023 18% 11%
a....
Assume you are considering a portfolio containing two assets, L and M. Asset L will represent...
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and M. Asset L will represent 56 % of the dollar value of the
portfolio, and asset M will account for the other 44 %. Assume that
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returns over the next 6 years, 2018dash2023, for each of these
assets are summarized in the following table:
Projected Return
Year
Asset L
Asset M
2018
14%
21%
2019
14%
17%...
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