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If an integer greater than 100 and less than 1,000 is to be
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29 Nov 2019, 03:22
29 Nov 2019, 03:22
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If an integer greater than 100 and less than 1,000 is to be selected at random, what is the probability that the integer selected will be a multiple of 7?
A. \(\frac{142}{999}\)
B. \(\frac{142}{900}\)
C. \(\frac{142}{899}\)
D. \(\frac{128}{900}\)
E. \(\frac{128}{899}\)
Kudos for the right answer and explanation
A. \(\frac{142}{999}\)
B. \(\frac{142}{900}\)
C. \(\frac{142}{899}\)
D. \(\frac{128}{900}\)
E. \(\frac{128}{899}\)
Kudos for the right answer and explanation
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Re: If an integer greater than 100 and less than 1,000 is to be
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29 Nov 2019, 06:53
29 Nov 2019, 06:53
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Carcass wrote:
If an integer greater than 100 and less than 1,000 is to be selected at random, what is the probability that the integer selected will be a multiple of 7?
A. \(\frac{142}{999}\)
B. \(\frac{142}{900}\)
C. \(\frac{142}{899}\)
D. \(\frac{128}{900}\)
E. \(\frac{128}{899}\)
Kudos for the right answer and explanation
A. \(\frac{142}{999}\)
B. \(\frac{142}{900}\)
C. \(\frac{142}{899}\)
D. \(\frac{128}{900}\)
E. \(\frac{128}{899}\)
Kudos for the right answer and explanation
We should start by asking "How many integers are greater than 100 and less than 1000?"
And other words, "How many integers are there from 101 to 999 inclusive?"
A nice rule says: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 101 to 999 inclusive = 999 - 101 + 1 = 899
So, we are randomly selecting one number from 899 integers
This tells us that the denominator of the probability must be 899
So we can eliminate answer choices A, B and D
We are left with answer choice C (142/899) and answer choice E (128/899)
Since the numerators are quite spread apart we can use some estimation.
There are 899 integers to choose from, and approximately 1/7 of those integers are multiples of 7
1/7 of 899 ≈ 128.4
So among the 899 integers, approximately 128 of them are multiples of 7.
So, P(select a multiple of 7) ≈ 128/899
So, the correct answer must be E
Cheers,
Brent
Re: If an integer greater than 100 and less than 1,000 is to be
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29 Nov 2019, 11:19
29 Nov 2019, 11:19
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Let's first count the total possible scenarios or events.
If an integer greater than 100 and less than 1,000 ==> means there is total (999-101+1)=899 numbers including 101 & 999.
Now 7*15=105 ; which is the immediate number after 101 which is divisible by 7
And 7*142=994 ; which is the last number before 999 which is divisible by 7
So (142-15+1)=128 numbers including 105 and 994 are divisible by 7.
so Probability = no of successful events/Total possible events= 128/899 ==> hence answer is (E).
If an integer greater than 100 and less than 1,000 ==> means there is total (999-101+1)=899 numbers including 101 & 999.
Now 7*15=105 ; which is the immediate number after 101 which is divisible by 7
And 7*142=994 ; which is the last number before 999 which is divisible by 7
So (142-15+1)=128 numbers including 105 and 994 are divisible by 7.
so Probability = no of successful events/Total possible events= 128/899 ==> hence answer is (E).
