Expected value = $0.17
Step-by-step explanation:
we find the probability of each numbers
Total numbers = 6
probability of 1 = 1/6
probability of 2 = 1/6
probability of 3 = 1/6
probability of 4 = 1/6
probability of 5 = 1/6
probability of 6 = 1/6
Expected value = sum of (the probabilty of each number × the amount for rolling each)
A win = positive while a loss is negative
no win or loss = 0
rolls a 1, wins $3; if she rolls a 2, she wins $1. If she rolls a 3,4, or5, she loses $1 and if a 6 is rolled, she doesn't win or lose
Expected value = (1/6 × 3) + (1/6 × 1) - (1/6 × 1) - (1/6 × 1) - (1/6 × 1) + (1/6 × 0)
= 3/6 + 1/6 - 1/6 - 1/6 -1/6 + 0 = 1/2 -2/6 = 1/2 - 1/3
Expected value = 0.5 - 0.33
Expected value = 0.17 (nearest cent)
Hence, it means Janet gained money.