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# What is the probability that a randomly selected integer from a list

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Math Expert
Joined: 02 Sep 2009
Posts: 58411
What is the probability that a randomly selected integer from a list  [#permalink]

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26 Mar 2018, 00:32
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Difficulty:

15% (low)

Question Stats:

89% (00:50) correct 11% (00:51) wrong based on 56 sessions

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What is the probability that a randomly selected integer from a list of consecutive integers from 101 to 500, inclusive will have a hundreds digit of 3?

(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 3/4

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Posts: 1153
Re: What is the probability that a randomly selected integer from a list  [#permalink]

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26 Mar 2018, 02:01
Bunuel wrote:
What is the probability that a randomly selected integer from a list of consecutive integers from 101 to 500, inclusive will have a hundreds digit of 3?

(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 3/4

Since the calculation we're required to do is straightforward, we'll just do it.
This is a Precise approach.

There are 400 integers between 101 to 500 inclusive of which exactly 100 (from 300 to 399, inclusive) have a hundreds digit of 3.
This gives a probability of 100/400 = 1/4.

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What is the probability that a randomly selected integer from a list  [#permalink]

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26 Mar 2018, 08:15
Bunuel wrote:
What is the probability that a randomly selected integer from a list of consecutive integers from 101 to 500, inclusive will have a hundreds digit of 3?

(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 3/4

Possible outcomes: 400
Possible: All integers from 101 to 500
(500 - 101) = 399 +1 = 400

Favorable outcomes: 100
Favorable: All the 300s. (399-300)= 99 + 1= 100

$$\frac{Favorable}{Possible}=\frac{100}{400}=\frac{1}{4}$$

*Inclusive counting ("add one before you're done") can create confusion. Inclusive counting: (Highest - lowest) + 1. If unsure in the moment, test with small numbers.
Ex.: How many integers from 1 to 4? List them: 1, 2, 3, 4. Count. There are four integers from 1 to 4.
Then: (4-1)= 3. Not correct. ADD 1. (3+1) = 4

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Re: What is the probability that a randomly selected integer from a list  [#permalink]

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26 Mar 2018, 08:32
total number = 500-101+1 = 400
favorable case = 100 ( from 300 to 399)
required probability = 100/400 = 1/4
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Re: What is the probability that a randomly selected integer from a list  [#permalink]

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27 Mar 2018, 11:33
Bunuel wrote:
What is the probability that a randomly selected integer from a list of consecutive integers from 101 to 500, inclusive will have a hundreds digit of 3?

(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 3/4

The number of integers from 101 to 500, inclusive, is 500 - 101 + 1 = 400.

The number of integers with a hundreds digit of 3 is 399 - 300 + 1 = 100.

Thus, the probability is 100/400 = 1/4.

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Re: What is the probability that a randomly selected integer from a list   [#permalink] 27 Mar 2018, 11:33
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