Three number are chosen from 1 to 20. Find the probability that they a

1.	Three number are chosen from 1 to 20. Find the probability that they are not consecutive.
Answer» Let ‘S’ be the sample space associated with the given experiment. Then– n(S) = ²⁰C₃ = 1140. Now, E = {(1, 2, 3), (2, 3, 4), (3, 4, 5),….., (18, 19, 20)} ⇒ n(E) = 18 ∴ P(E) = \(\frac{n(E)}{n(S)}=\frac{18}{1140}=\frac{3}{190}\) ∴ P(E’) = 1 − \(\frac{3}{190}=\frac{187}{190}\) ∴ The required probability = \(\frac{187}{190}\).

Three number are chosen from 1 to 20. Find the probability that they are not consecutive.

Answer»

Let ‘S’ be the sample space associated with the given experiment. Then–

n(S) = ²⁰C₃ = 1140.

Now, E = {(1, 2, 3), (2, 3, 4), (3, 4, 5),….., (18, 19, 20)}

⇒ n(E) = 18

∴ P(E) = \(\frac{n(E)}{n(S)}=\frac{18}{1140}=\frac{3}{190}\)

∴ P(E’) = 1 − \(\frac{3}{190}=\frac{187}{190}\)

∴ The required probability = \(\frac{187}{190}\).

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Three number are chosen from 1 to 20. Find the probability that they are not consecutive.

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