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If an integer from 1 through 1000 is chosen at random then find the probability that the integer is multiple if 2 or multiple of 9? Give me a answer in full statement?

Posted by Unknown . 5 years ago

CBSE > Class 09 > Mathematics

3 answers

Mukul Kumar 😎 5 years, 2 months ago

Why did you subtract 55 from the sum of 500 and 111

Unknown . 5 years, 2 months ago

Thank u yr

Yogita Ingle 5 years, 2 months ago

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)

Required probability = n(E)/n(S) = 556/1000 = 0.556

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