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A number is randomly chosen from the first 100 positive integers. What

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A number is randomly chosen from the first 100 positive integers. What  [#permalink]

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New post 03 Jan 2019, 03:48
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A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3?


(A) 32/100

(B) 33/100

(C) 1/3

(D) 34/100

(E) 2/3

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Re: A number is randomly chosen from the first 100 positive integers. What  [#permalink]

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New post 03 Jan 2019, 05:12
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Total number ways of choosing a number from the first 100 positive integer = 100 ways
Total number of multiples of 3 between 1 and 100 is 33, i.e. 3, 6, 9....99 = 33 multiples
Hence, the number ways of choosing a multiple of 3 from the first 100 positive integer = 33 ways
Therefore, when a number is randomly chosen from the first 100 positive integers, the probability that it is a multiple of 3 = 33/100

Hence, the Correct Answer is Option B. 33/100

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Re: A number is randomly chosen from the first 100 positive integers. What  [#permalink]

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New post 03 Jan 2019, 05:44
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Given : A number is randomly chosen from the first 100 positive integers.
Question : What is the probability that it is a multiple of 3?

We need to find the number of multiples of 3 in first 100 POSITIVE integers.
By AP we have
Tn = a + (n-1)*d (where, Tn = 99; a= 3; d =3)
99 = 3 + (n-1)* 3
96 = (n-1)* 3
32 = (n-1)
n = 33

Therefore, the probability that chosen number in first 100 is a multiple of 3 is given by
= No. of favorable outcomes / Total no. of outcomes
= 33 / 100
Answer Option B is Correct.
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Re: A number is randomly chosen from the first 100 positive integers. What  [#permalink]

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New post 03 Jan 2019, 05:47
Bunuel wrote:
A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3?


(A) 32/100

(B) 33/100

(C) 1/3

(D) 34/100

(E) 2/3



No of Possibilities = 100
Multiples of 3 from 1 to 100 = 33

Hence, Probability = 33/100
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Re: A number is randomly chosen from the first 100 positive integers. What  [#permalink]

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New post 06 Jan 2019, 04:26
Bunuel wrote:
A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3?


(A) 32/100

(B) 33/100

(C) 1/3

(D) 34/100

(E) 2/3




33 multiples of 3 from 1 to 100
so
33/100 would be the P of multiples of 3 in between 1 to 100

IMO B
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A number is randomly chosen from the first 100 positive integers. What  [#permalink]

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New post 06 Jan 2019, 04:30
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1
A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3?

EASY FORMULA FOR SUCH QUESTIONS:

1+ [ {last multiple of increment in the given range - first multiple of the increment in the range} / increment ]

Here increment = 3
range = 1-100 (first 100 positive numbers)

Answer = 1+ [ {99-3} / 3 ]
= 1+ 96/3
= 1+ 32
= 33

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A number is randomly chosen from the first 100 positive integers. What &nbs [#permalink] 06 Jan 2019, 04:30
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