An eccentric millionaire decided to give away $1,000,000 if Janelle took one die and rolled a "4". He wanted Janelle to have a better than 1 in 6 chance of winning, so before she rolled the die he told her that she could roll the die 3 times. If any roll was a "4", she would win the million dollars. What are Janelle's chances of winning the million dollars?
Chance of winning each roll is 1/6. Which means the chances of losing each roll are 1 - 1/6 = 5/6
Calculate the probability of 3 straight losing rolls:
P(Lose) = P(Loser) * P(Loser) * P(Loser) = 5/6 * 5/6 * 5/6 = 125/216
P(Win) = 1 - P(Lose)
P(Win) = 1 - 125/216
P(Win) = 216/216 -125/216
P(Win) = 91/216
Chance of winning each roll is 1/6. Which means the chances of losing each roll are 1 - 1/6 = 5/6
Calculate the probability of 3 straight losing rolls:
P(Lose) = P(Loser) * P(Loser) * P(Loser) = 5/6 * 5/6 * 5/6 = 125/216
P(Win) = 1 - P(Lose)
P(Win) = 1 - 125/216
P(Win) = 216/216 -125/216
P(Win) = 91/216