In a certain year, 88% of all Caucasians in the U.S., 77% of all African-Americans, 77% of all Hispanics, and 74% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 68% Caucasian, 10% African-American, and 10% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic? (Round your answer to the nearest whole percent.)

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Asked Dec 1, 2019
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In a certain year, 88% of all Caucasians in the U.S., 77% of all African-Americans, 77% of all Hispanics, and 74% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 68% Caucasian, 10% African-American, and 10% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic? (Round your answer to the nearest whole percent.)

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Expert Answer

Step 1

Let A be the event of Caucasians, B be the event of sleeting African-Americans, C be the event of selecting Hispanics and D be the event of other in the US that used the internet for email.

Hence the probability of selecting any group is equally likely and mutually exclusive.

That is, P (A) = 0.88, P(B) = 0.77 , P(C) = 0.77 and P(D) = 0.74.

It is given that the U.S population Caucasian has 68%, U.S population has African-American has 10% , U.S population Hispanic has 10% and The percentage of American not classified into any of this group is (1– 0.68 – 0.10 – 0.10)*100 = 12%

Let S be the event that the selected U.S residents that used internet, then the priory probability are,

P(S|A)= 0.68, P(S|B) = 0.10, P(S|C) = 0.10 and P(S|D) = 0.12

The percentage of U.S residents that used internet is

P(S) P(A)P(S/A)+ P(B)P (S / B)+ P(C) P (S/C)+P(D) (S |D)
=0.88(0.68)+0.77(0.10) +(0.77) (0.10) +0.74 (0.12)
0.5984 0.077 0.077 0.0888
0.8412
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P(S) P(A)P(S/A)+ P(B)P (S / B)+ P(C) P (S/C)+P(D) (S |D) =0.88(0.68)+0.77(0.10) +(0.77) (0.10) +0.74 (0.12) 0.5984 0.077 0.077 0.0888 0.8412

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Step 2

The proportion of U.S residents who used the ...

P(C) P(S/C)
P(A) P(S/A)+P(B) P (S / B) + P (C) P(S/C)+P(D) (S| D)
P(C|S)=
(0.77)(0.10)
0.88 (0.68)+0.77(0.10) +(0.77)(0.10) + 0.74(0.12)
0.077
0.8412
=0.0915
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Image Transcriptionclose

P(C) P(S/C) P(A) P(S/A)+P(B) P (S / B) + P (C) P(S/C)+P(D) (S| D) P(C|S)= (0.77)(0.10) 0.88 (0.68)+0.77(0.10) +(0.77)(0.10) + 0.74(0.12) 0.077 0.8412 =0.0915

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