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.

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orchestra answered 1 year ago
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