Question

Information about mutual funds provided by Morningstar Investment Research includes the type of mutual fund (Domestic Equity, International Equity or Fixed Income) and the Morningstar rating for each fund. The ratings is expressed from a 1-star (lowest rating) to a 5-star (highest rating). A sample of 25 mutual funds was selected from the Morningstar Funds 500 and the following information was obtained:

� Sixteen funds were Domestic Equity
� Thirteen mutual funds were rated 3-star or less
� Seven of the Domestic Equity fund were rated 4-star
� Two of the Domestic Equity funds were rated 5-star
Assume that one of these 25 mutual funds will be randomly selected in order to learn more about the mutual fund and its investment strategy.
a. What is the probability of selecting a Domestic Equity Fund?
b. What is the probability of selecting a fund with a 4 or 5-star rating?
c. What is the probability of selecting a fund that is both a Domestic Equity Fund and a fund with a 4 or 5-star rating?
d. What is the probability of selecting a fund that is a Domestic Equity Fund or a fund with a 4 or 5-star rating?

Answer 1

The probability of selecting a Domestic Equity Fund is 0.64. The probability of selecting a fund with a 4 or 5-star rating is 0.36. The probability of selecting a fund that is both a Domestic Equity Fund and a fund with a 4 or 5-star rating is 0.36.

Step-by-step explanation:

a. To find the probability of selecting a Domestic Equity Fund, you need to divide the number of Domestic Equity funds by the total number of mutual funds. In this case, there are 16 Domestic Equity funds out of a total of 25 mutual funds. Therefore, the probability of selecting a Domestic Equity Fund is 16/25 or 0.64.

b. To find the probability of selecting a fund with a 4 or 5-star rating, you need to add the number of funds rated 4-star and 5-star, and then divide that sum by the total number of mutual funds. In this case, there are 7 Domestic Equity funds rated 4-star, 2 Domestic Equity funds rated 5-star, and a total of 25 mutual funds. Therefore, the probability of selecting a fund with a 4 or 5-star rating is (7+2)/25 or 0.36.

c. To find the probability of selecting a fund that is both a Domestic Equity Fund and a fund with a 4 or 5-star rating, you need to count the number of funds that meet both criteria and divide it by the total number of mutual funds. In this case, there are 7 Domestic Equity funds rated 4-star, 2 Domestic Equity funds rated 5-star, and a total of 25 mutual funds. Therefore, the probability of selecting a fund that is both a Domestic Equity Fund and a fund with a 4 or 5-star rating is (7+2)/25 or 0.36.

d. To find the probability of selecting a fund that is a Domestic Equity Fund or a fund with a 4 or 5-star rating, you need to add the probabilities of selecting a Domestic Equity Fund and a fund with a 4 or 5-star rating, and then subtract the probability of selecting a fund that is both a Domestic Equity Fund and a fund with a 4 or 5-star rating. In this case, the probability of selecting a Domestic Equity Fund is 0.64, the probability of selecting a fund with a 4 or 5-star rating is 0.36, and the probability of selecting a fund that is both a Domestic Equity Fund and a fund with a 4 or 5-star rating is 0.36. Therefore, the probability of selecting a fund that is a Domestic Equity Fund or a fund with a 4 or 5-star rating is 0.64+0.36-0.36 or 0.64.

Answer 2

(a)0.64

(b)0.48

(c)0.3072

(d)0.76

Step-by-step explanation:

Domestic Equity funds= 16

Funds rated 3-star or less=13

Domestic Equity fund were rated 4-star=7

Domestic Equity funds were rated 5-star=2

Total Sample of Funds taken=25

Domestic Equity Funds+International Equity=25

16+International Equity Funds=25

International Equity or Fixed Income Funds =9

For, Domestic Equity Funds (16)

Funds Rated 5 Stars = 2

Funds Rated 4 Stars=7

Therefore, Funds Rated 3 Stars=16-9=7

Since 13 mutual funds were rated 3 Stars or less,

Domestic Equity Funds Rated 3 Stars + International Equity Rated 3 Stars =13

7+International Equity Rated 3 Stars=13

International Equity Rated 3 Stars=13-7=6

International Equity or Fixed Income(9)

Rated 3 Stars=6

Rated 4 or 5 Stars=9-6=3

(a)Probability of selecting a Domestic Equity Fund

Number of Domestic Equity Funds=16

Total Sample of Funds=25

P(selecting a Domestic Equity Fund) = [TeX]\frac{16}{25}[/TeX]=0.64

(b)Probability of selecting a fund with a 4 or 5-star rating.

International Equity Rated 4 or 5 Stars=3

Domestic Equity Funds Funds Rated 4 or 5 Stars = 2+7=9

Total Funds Rated 4 or 5 Stars=3+9=12

Therefore:

P(selecting a fund with a 4 or 5-star rating)=[TeX]\frac{12}{25}[/TeX]=0.48

(c)Probability of selecting a fund that is both a Domestic Equity Fund and a fund with a 4 or 5-star rating.

Number of Domestic Equity Funds=16

Total Funds Rated 4 or 5 Stars=12

P(Domestic Equity Fund AND a fund with a 4 or 5-star rating)

= [TeX]\frac{16}{25} X \frac{12}{25}[/TeX]=0.3072

(d)Probability of selecting a fund that is a Domestic Equity Fund or a fund with a 4 or 5-star rating.

Note:

P(A or B)= P(A)+P(B)-P(A AND B)

Number if Domestic Equity Funds rated 4 or 5 Stars=9

= [TeX]\frac{16}{25} + \frac{12}{25} -\frac{9}{25} [/TeX]=0.76