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# a pair of fair dice is tossed 3 times. find the probability a seven appears 3 times   ⚑ Flag

by Virginia037 at November 20, 2010

## Answers

Virginia - First let's look at what goes in the denominator ... this is called your "sample space". The first dice has 6 possible outcomes, agree?  They are {1,2,3,4,5,6}. The second dice also has the same 6 possible outcomes. Since the tossing of the first and second dice are "independent" events, you simply multiply to get the total number of outcomes ( 6 ways times 6 ways = 36 possible outcomes).  Try writing out the 36 possible outcomes to convince yourself this makes sense. Finally, tossing the "pair" of dice 3 times results in 36x36 x36 possible outcomes so your numerator (the total sample space) will equal 46,656 possible outcomes. Next, let's look at the numerator.  Well, we have {(1,6),(2,5),(3,4),(6,1),(5,2),(4,3)}, where the first value is the number of dots on the first dice and the second value is the number of dots on the second dice.  In total, we have 6 possible outcomes that add up to 7 on one toss or 6x6x6 = 216 ways when tossing the dice 3 times. Hope this helps!

Steve204 November 20, 2010

There are 6 x 6 = 36 possible outcomes for rolling two dice.  There are 6 possible ways to roll a total of seven, as stated below.  Thus, for each roll of the dice, there is a 6/36 or 1/6 probability of rolling a seven.  The probability of it happening on three tosses is 1/6 x 1/6 x 1/6 = 1/216.

Bill201 November 22, 2010

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