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Probability — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSProbability3 Marks
Question
Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.
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Answer

We have integers 1, 2, 3, …., 1000
We have integers 1, 2, 3, ….., 1000
n(S) = 1000
Number of integers which are multiple of 2 = 500 Let the number of integers which are multiple of 9 be n.
nth term = 999
⇒ 9 + (n -1)9 = 999
⇒ 9 + 9n - 9 = 999
⇒ n = 111
From 1 to 1000, the number of multiples of 9 is 111.
The multiple of 2 and 9 both are 18, 36, …., 990.
Let m be the number of terms in above series.
mth term = 990
⇒ 18 + (m - 1)18 = 990
⇒ 18 + 18m - 18 = 990
⇒ m = 55
Number of multiples of 2 or 9 = 500 + 111 - 55 = 556 = n(E)
$\therefore\ \text{Required probability}=\frac{\text{n}(\text{E})}{\text{n}(\text{S})}$
$=\frac{556}{1000}=0.556$

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