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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

Respuesta :

pedrocarratore

Answer:

(E) 29.0

Step-by-step explanation:

If a tag is drawn at random from each box, the expected value of the sum of the tags is the sum of the expected values for each tag.

The expected value for each tag is the mean value of the numbers in its box.

[tex]EV = \frac{1+2+3+4+5+6+7+8+9+10}{10} +\frac{20+21+22+23+24+25+26+27}{8} \\EV = 5.5 +23.5\\EV= 29[/tex]

The expected value of the sum of the numbers on the two selected tags is 29.

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