Mr van Rooyen has entered a game where he will win the star prize if he throws three sixes in a row with a single six-sided dice. He’s brought along his loaded dice where the chance of throwing a six is double the chance of throwing any one of the other five numbers. If Mr van Rooyes uses his loaded dice, how much more likely is he to win the star prize compared a normal dice? Twice as likely? Three times as likely? Five times as likely? Ten times as likely?
Five times as likely The chances of throwing a six three times in a row is 1/6 x 1/6 x 1/6 = 0.00463, ie 463 times out of 100,000. With the loaded dice, there’s six sides with one side having twice the chance of being thrown. So each side except six has a 1 in 7 chance of being thrown and the six has a 2 in 7 chance. So the chances of throwing a six three times in a row is 2/7 x 2/7 x 2/7 = 0.02332, ie 2332 times out of 100,000. Which is 2332/463 = 5.04, ie roughly five times as likely