WorkSheet 5

1 . Fair and Unfair Dice

If the die is fair , then each face will have the probability of 1 /6 each time a die is cast . If we roll the die 10 times , the probability that the face would be 6 each time would be . We have the 6 combinations out of dice . So the probability of having the sum of 7 would be 1 /6

On the other hand , in to have a sum 0f 12 , we need to have 6 on each cast . Out of the thirty six possibilities , we only have one

br combination . The probability of having the sum of 12 is 1 /36

I should switch to maximize my chance of winning the Ferrari . Let A B , C represent the 3 doors . Initially , each door will have the probability of 1 /3 . Without loss of generality , say the Ferrari is on door C then A , B will reveal a sheep behind the door . Then we would only have three cases

If I choose C , then the quiz master can show either A or B which will reveal the sheep . If I decide to switch , then I would lose . But if I stay with door C , then I win

If I choose B , then the quiz master has to show to A as he knows that the ferrari is behind C . If I switch , then I would win the car Otherwise , I would lose

The third case would be , if...