In a game called Taxation and Evasion a player rolls a pair

. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited at least once is ________.

Solution

Probability of getting audited = prob of getting 7 + prob of getting 11 + prob getting 12

                                              = 6/36 + 2/36 + 1/36

                                              = 0.25

Probability of not getting audited = 1-0.25 = 0.75

probability that she gets audited at least once in 5turns = 1 - prob that she doesn\'t get audited at all

                                                                                        = 1 - 5C0 * 0.75⁰ * 0.25⁵

                                                                                        = 0.999