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Suppose that two.integers from the set of 8 integrs {1,2,3....8} are chosen at random. Find the probability that i. both numbers match. ii. Sun of the two numbers picked is less than 4?

 Aug 3, 2020
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I will assume that they are chosen "with replacement" -- which means that after the first number is chosen, it is put back into the set so that it has a possibility of being chosen again.

 

i)  Once the first number is chosen, the probability that the second number matches the first number is 1/8.

 

ii)  There are 8 possibilities for the first number and 8 possibilities for a total of 8 x 8 = 64 possibilities.

     Of these possibilities, 1,1  1,2  2,1  are the only ones that have a sum less than 4:  3/64.

 Aug 3, 2020

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