Question

a box contains 10 equal-sized balls, numbered 1 to 10. two balls are drawn at random simultaneously. what is the probability that the numbers on the two balls will differ by more than 2?

Answer 1

The probability that the two balls are chosen will differ by more than 2 is 43/45

Probability is the likelihood or chance that an event will occur.

If a box contains 10 equal-sized balls and 2 balls are chosen at random from the box, the total outcome will be expressed as:

$10C_2=\frac{10!}{(10-2)!2!}\\ 10C_2=\frac{10!}{8!2!}\\10C_2=\frac{10\times 9 \times 8!!}{8!2!}\\10C2=\frac{90}{2} =45 ways$

If the number on the two balls chosen will differ by less than or equal to 2, the expected outcomes are (1, 2), (1, 3) that is 2 outcomes

The probability that the two balls are chosen will differ by less than or equal to 2 is 2/45

The probability that the two balls are chosen will differ by more than 2 is 1 - 2/45 = 43/45

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