You are a financial analyst facing the task of selecting bond mutual funds to pu

Question

You are a financial analyst facing the task of selecting bond mutual funds to purchase for a client's portfolio. You have narrowed the funds to be selected to fourteen different funds. In order to diversify your client's portfolio, you will recommend the purchase of three different funds. Six of the funds are short-term corporate bond funds. What is the probability that of the three funds selected,

a. exactly 1 is a short-term corporate bond fund?

b. at least 1 is a short-term corporate bond fund?

c. two are short-term corporate bond funds?

d. Another financial analyst narrowed their own funds to be selected to ten different funds. The probability that the three of the recommended funds were exactly two of the six short-term corporate bond funds is 50.00 %. How does this compare to the results of c. ?

a. P(X= 1) = __________(Round to two decimal places as needed.)

b. P(X 1)= ___________(Round to two decimal places as needed.)

c. P(X=22 )= ____________(Round to two decimal places as needed.)

Explanation / Answer

Ans:

There are total 14 funds.

out of these 6 are short term corporate bond funds

We have to select 3 funds.

a)Probability that excatly one is short term corporate bond funds=

6C1*8C2/14C3

=6*28/(14*13*12/6)

=1008/2184

=0.4615

b)Probability of atleast one corporate short term bond=1-P(none is corporate short term bond)

=1-(8C3/14C3)

=1-(8*7*6/14*13*12)

=1-(336/2184)

=1-0.1538

=0.8462

c)Probabilty that 2 are short term corporate fund=(6C2*8C1)/14C3

=120*6/14*13*12

=720/2184

=0.3297

d)d)It will be more than the probability of part c

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