One number is randomly selected from the natural numbers 1 to 100. Fin

1.	One number is randomly selected from the natural numbers 1 to 100. Find the probability that the number selected is either a single digit number or a perfect square.
Answer» One number is randomly selected from the numbers 1 to 100. ∴ Total number of primary outcomes, n = ¹⁰⁰C₁ = 100 A = Event that the number selected is a single digit number = {1. 2,3, 4,5,6,78, 9} ∴ m = 9 ∴ P(A) =\(\frac{ m}{n} = \frac{9}{100}\) B = Event that the number selected is a perfect square = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100) ∴ m = 10 ∴ P(B) = \(\frac{ m}{n} = \frac{10}{100}\) A ∩ B = Event that the selected number is a single digit number and a perfect square = {1, 4,9} ∴ m = 3 ∴ P(A ∩ B) = \(\frac{m}{n}=\frac{3}{100}\) Now, A ∪ B = Event that the number selected is either a single digit number or a perfect square ∴ P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = \(\frac{9}{100}+\frac{10}{100}−\frac{3}{100}\) = \(\frac{16}{100}=\frac{4}{25}\)

One number is randomly selected from the natural numbers 1 to 100. Find the probability that the number selected is either a single digit number or a perfect square.

Answer»

One number is randomly selected from the numbers 1 to 100.

∴ Total number of primary outcomes,

n = ¹⁰⁰C₁ = 100

A = Event that the number selected is a single digit number

= {1. 2,3, 4,5,6,78, 9}

∴ m = 9

∴ P(A) =\(\frac{ m}{n} = \frac{9}{100}\)

B = Event that the number selected is a perfect square

= {1, 4, 9, 16, 25, 36, 49, 64, 81, 100)

∴ m = 10

∴ P(B) = \(\frac{ m}{n} = \frac{10}{100}\)

A ∩ B = Event that the selected number is a single digit number and a perfect square

= {1, 4,9}

∴ m = 3

∴ P(A ∩ B) = \(\frac{m}{n}=\frac{3}{100}\)

Now, A ∪ B = Event that the number selected is either a single digit number or a perfect square

∴ P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= \(\frac{9}{100}+\frac{10}{100}−\frac{3}{100}\)

= \(\frac{16}{100}=\frac{4}{25}\)

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