Question

theme: random variables, probability distributions and expected valueJanet plays a dice game. If she rolls a 1, she wins $3 while 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. Find the expected value of this dice game. •Round to the nearest cent. Do not round until the final calculation.

Answer 1

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.