Suppose we make 20 tosses using 2 dice. What is the probability of scoring a two numbers that sum to 7?(adsbygoogle = window.adsbygoogle || []).push({});

My attempt

The sample space for a single toss of a single die is S = {1, 2, 3, 4, 5, 6}

For a single toss of both dice, the sample space is

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

The sample points with sum 7 are:

(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)

These are 6 possibilties out of 36.

So for *each toss* of the 2 dice, there is a 6/36 probability of scoring two numbers that sum to 7.

My question is, how to we work out what the probabilty would be for 20 tosses?

If we have 20 tosses, then there are a total of 36*20 = 720 possible sample points. But how many of those possibilities contain numbers that sum to 7?

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# Probability with 2 dice

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