Please help to solve this probability problem. The numbers on
the line (excluding the
question numbers like 1. 2. 3.) are the
final correct answers (for this
question, the correct answers are
2.83, 3.50 and 2.68 respectively). Please give detailed steps to
explain how to get the final correct answer. Thanks!
- Please Help To Solve This Probability Problem The Numbers On The Line Excluding The Question Numbers Like 1 2 3 Ar 1 (279.66 KiB) Viewed 57 times
6. Fill in the blanks We play a game with a dice which is biased in such a way that it shows: • 1,2,3 with probability 10% each, • 4,5 with probability 20% each, • 6 with probability 30%. The game starts with an initial roll of the dice. • If the initial roll is a 6, we lose, and the game ends. • If the initial roll is k € {1,2,3}, the dice is rolled k additional times: o If the value 6 occurs at least once in these additional rolls, we lose, and the game ends. o Otherwise, the game is continued with a fresh initial roll. • If the initial roll is k = {4,5}, the dice is rolled repeatedly until the value k or the value 6 occurs: o If the value 6 occurs, we lose, and the game ends. o If the value k occurs, we win, and the game ends. The dice rolls are assumed to be independent. The random variable R denotes the number of rolls of the dice. (2 decimal places) E[R] 1. 2.83 E[R|we win E[Rwe lose 2. 3.50 (2 decimal places) 3. 2.68 (2 decimal places)