Suppose you roll 6 ’fair’ dice (each has six sides numbered 1 to 6 and each side has an equal 1/6 probability of showing). Let event A be the case where exactly two dice show a number less than 3 (1 or 2). Let event B be the case where where exactly two dice show a number greater than 4 (5 or 6)) Let event C be the case where every die shows a different number. a. What is probability of rolling the 6 dice and seeing both the A and B conditions? b. What is probability of rolling the 6 dice and seeing the C condition? c. What is probability of rolling the 6 dice twice and seeing the C condition in both rolls? Suppose you now roll 12 ’fair’ dice (not 6 dice rolled 2 times; you use 12 distinct dice) d. What is probability of seeing exactly 2 dice for each number (1 to 6)? e. Explain why the answer to d is the either the same or not the same as the answer to c?
Suppose you roll 6 ’fair’ dice (each has six sides numbered 1 to 6 and each side has an equal 1/6
Given the experiment of rolling 6 fair dice and the events A, B and C are denotes
Event A : exactly two dice show a number less than 3 (1 or 2)
Event B : exactly two dice show a number greater than 4 (5 or 6)
Event C : every die shows a different number
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