Remember that
The expected value (EV)is the probability of winning multiplied by the value you get when you win, plus the probability of losing multiplied by the value you get when you lose (which is negative as it is a loss)
we have that
The probability that chooses any ball is P=1/8
so
EV=(1)(1/8)+(2)(1/8)+(5)(1/8)+6(1/8)+(8)(1/8)+(10)(1/8)-(13)(1/8)-(13)(1/8)
Factor 1/8
EV=(1/8)[1+2+5+6+8+10-13-13]
EV=(1/8)[6]
EV=$0.75
The answer to Part a is 0.75 dollars
Part b
we have that
The EV is positive
that means
Heather can expect to gain money
She can expect to win 0.75 dollars per selection