1. A recent survey of banks revealed the following distribution for the interest rate being charged on a home?

loan (based on a 30-year mortgage with a 10% down payment).


Interest Rate 7.0% 7.5% 8.0% 8.5% %26gt;8.5%


Probability 0.12 0.23 .24 .35 0.06





2. If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%?





3.The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is





4.The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is

1. A recent survey of banks revealed the following distribution for the interest rate being charged on a home?
2. If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%?


.35 +.06 = .41


41%





3. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is





400 college degrees + 100 single - 60 overlap = 440 single or college





4.The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is





p(a) = .25


p(b) = .74


p(a or b) = .89


p(a and b) = .74 + .25 - .89 = .10


10%
Reply:this is just a discrete distribution...exceeds 8%...so what is the probability that it's going to be 8.5% or greater (the word "exceeds" here implies that you're looking for the probability that it's going to be strictly greater than 8%), and these are disjoint sets, so it's just the sum:


P(interest = 8.5%) + P(interest %26gt; 8.5%) = 0.35 + 0.06 = 0.41





3. this can be solved by inclusion/exclusion, i believe...





so # that are either single or college graduates...well, you know 400 had college degrees...100 are single...60 are single college graduates...


so #(either single or college grads) = #(single) + #(college grads) - #(single college grads) = 400 + 100 - 60 = 440





divide this by the total number of employees, namely 600, to get P(single or college grad) = 440/600 = 11/15





4)


inclusion/exclusion again...


P(house sales increase) + P(loan rates increase) - P(house sales AND loan rates increase) = P(house sales increase OR loan rates increase)





or working with knowns,





P(house sales increase) + P(loan rates increase) - P(house sales increase OR loan rates increase) = P(house sales AND loan rates increase)





plug in what you know:





0.25 + 0.74 - 0.89 = 0.10 = P(house sales AND loan rates increase)





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A note about inclusion/exclusion:





the reason you do this is so that you're not counting pieces more than once...like say you have A and B, denote the intersection as Int(A,B), and the union as U(A,B)...so the number of items in U(A,B) is going to be the number in A plus the number in B, minus whatever's counted twice, namely the ones in both A and B..in mathematical terms, you get


U(A,B) = A + B - Int(A,B)...and you can do this with as many sets as you wish, although the things get messier...for 3 sets,





U(A,B,C) = A + B + C - Int(A,B) - Int(B,C) - Int(A,C) + Int(A,B,C)