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:
[tex]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[/tex]
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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