Solution:
Given that;
Laura is playing a game of chance in which she tosses a dart into a rotating dart board with 8 equal-size slices numbered 1 through 8
a) For the expected value;
If Laura tosses the dart once, and she wins $1 if the dart lands in slice 1, $3 if the dart lands in slice 2, $5 if the dart lands in slice 3, $8 if the dart lands in slice 4, and $10 if the dart lands in slice 5 and loses she loses $9 if the dart lands in slices 6, 7, or 8
The expected value will be
[tex]Expected\text{ value}=\frac{1(1)+3(1)+5(1)+8(1)+10(1)+9(3)}{8}=\frac{27-27}{8}=\frac{0}{8}=0[/tex]Hence, the expected value is $0
b) If Laura plays many games, she is expected to neither gain nor lose money.
This is because she has 5 out of 8 chances to win some money and the expected value is $0t
Hence, Laura can expect to break even (neither gain nor lose money)