Question

You throw two fair dice, one green and one red, and observe the numbers that came up.Take event A: the sum is 7, and event B: the red die comes up even. Are these two events independent?

Answer 1

Following is the sample space when we roll two fair dice (first green and second green),

Since there are 36 outcomes, out of which 6 outcomes have sum 7. Let A shows the event that sum is 7 so

P(A) = 6/36 = 1/6

There are 18 outcomes in event B so,

P(B) = 18/36 = 1/2

Out of 36 outcomes 3 outcomes have sum 7 and red die has even so

P(B and A) = 3/36 =1/12

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So,

P(A)P(B) = (1/6) * (1/2) = 1/12

Since

P(A and B) = P(A)P(B)

So A and B are independent.