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?
Accepted Solution
A:
Answer:The expected value of the sum of the numbers on the two selected tags is 29.Step-by-step explanation:Given : A box contains 10 tags, numbered 1 through 10, with a different number on each tag. Let [tex]X_1=1[/tex] and [tex]X_2=10[/tex]A second box contains 8 tags, numbered 20 through 27, with a different number on each tag.Let [tex]Y_1=20[/tex] and [tex]Y_2=27[/tex]One tag is drawn at random from each box. To find : What is the expected value of the sum of the numbers on the two selected tags?Solution : The expected value of the sum of the numbers on the two selected tags is given by, [tex]E(X)=\frac{X_1+X_2}{2}+\frac{Y_1+Y_2}{2}[/tex][tex]E(X)=\frac{1+10}{2}+\frac{20+27}{2}[/tex][tex]E(X)=\frac{11}{2}+\frac{47}{2}[/tex][tex]E(X)=5.5+23.5[/tex][tex]E(X)=29[/tex]Therefore, the expected value of the sum of the numbers on the two selected tags is 29.