Please provide solution for the questions from practice question ( Quiz 1) for the subject Quantitative Analysis

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If the probability of both a Airport and Five star Hotel being built in 2 months is 70% and the probability of a airport built is 80%, what is the probability of Five start hotel being built if a airport is built?

Select one:
a. 88%
b. 60%
c. 56%
Incorrect
d. 72%

The probability of A is 0.4. The probability of AD is 0.6. The probability of (B|A) is 0.5, and the probability of (B|AD) is
0.2. Using Bayes’ formula, what is the probability of (A|B)?

Select one:
a. 0.25
b. 0.62
c. 0.37
d. 0.85

X and Y are discrete random variables. The probability that X = 4 is 0.20 and the probability that Y = 5 is 0.30. The probability of observing that X = 4 and Y = 5 is closest to:

Select one:
a. 0.5
b. Cannot answer with the given data
c. 1
d. 0.6

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Posted by Dipti (Questions: 1, Answers: 1)
Asked on March 4, 2015 12:03 am
Category: FRM Part I
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The correct answer for 1st question will be a.88%. As P(AB) = P(A|B) x P(B).
So, = .70/.80 = .875 or .88

Question: 2

We need to apply total probability rule with that we can compute the P(B):
P(B) = [P(B|A) × P(A)] + [P(B|AD) × P(AD)]
P(B) = [0.5 × 0.4] + [0.2 × 0.6] = 0.32

Note: here AD is just a symbol. Which is telling if A is price increase than AD is no price increase. It’s a typo error.

Using Bayes’ formula as given in the notes, we can solve for P(A|B):
P(A|B) = [ P(B|A) / P(B) ] × P(A) = [0.5 / 0.32] × 0.4 = 0.625

Question: 3

If you knew that X and Y were “independent”, you could calculate the probability as 0.20(0.30) = 0.06. So, Without this
knowledge, you would need to know the joint probability distribution.

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Posted by pravin Khetan (Questions: 0, Answers: 7)
Answered on March 4, 2015 5:17 pm
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