A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags (A) 13.5 (B) 14.5 (C) 15.0 (D) 27.0 (E) 29.0

E) 29.0

Step-by-step explanation:

The value of the sum is obtained from 2 independent experiments: the value of the number of the first box X₁ and the value of the number of the second box X₂.

The expected value of a draw is the average of all its values, so E (X₁) = (1+2+3+4+5+6+7+8+9+10) / 10 = 5.5 and E (X₂) = (20+21+22+23+24+25+26+27) / 8 = 23.5

Hence, E (X₁+X₂) = E (X₁) + E (X₂) = 5.5+23.5=29