8 A box contains 10 balls numbered 1 2 10 Suppose that tw

8. A box contains 10 balls numbered 1, 2, . . ., 10. Suppose that two balls are selected at random without replacement from this box and the numbers on the balls are noted. Find the probability that the numbers on the two balls differ by 2 or more.

9. Redo problem 8 assuming that the two balls are selected with replacement.

I have a feeling that I\'m closing in on the answer to the first part (number 8) but the \"or more\" part has me concerned.

I\'d really appreciate thorough answers with an explanation. I\'m honestly not very concerned with the final answer. I\'d like to know how to get there.

Solution

8.

P(differ by 2 or more) = 1 - P(consecutive balls)

Now, there are 10C2 = 45 ways to choose any 2 balls.

There are 9 ways to choose 2 consecutive numbered balls.

Thus,

P(differ by 2 or more) = 1 - 9/45 = 0.8 [ANSWER]

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