I want to know how can we approach questions of this type ?
What is the probablity of selecting a 6 digit number such that the fourth digit is the same as first digit , second digit is the same as fifth digit and third digit is the same as 6th digit ?
do not have the answer options available ....
can someone please tell me how to proceed with this ?
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Hi abhasjha,
These types of questions are always carefully written, so you have to pay attention to the details and you have to think about the limitations for each digit.
For example, a 6-digit number won't start with a 0, but the other digits could be 0 (unless it's a numerical code, then it MIGHT be able to start with a 0). Here, I'll assume that the intent is to ask for a 6-digit number with no special rules to consider besides the ones that you listed....
The possible 6-digit numbers are 100,000 - 999,999, inclusive, so there are 900,000 possible numbers.
We're asked for the probability of finding a very specific type of 6-digit number
1st Digit: 1-9 = 9 possibilities
4th Digit: MUST match the 1st = 1 possibility (once we know the first digit)
2nd Digit: 0-9 = 10 possibilities
5th Digit: MUST match the 2nd = 1 possibility (once we know the second digit)
3rd Digit: 0-9 = 10 possibilities
6th Digit: MUST match the 3rd = 1 possibility (once we know the third digit)
So....(9)(10)(10)(1)(1)(1) = 900 possibilities that match the description
900/900,000 = 1/1,000 = the probability of finding the 6-digit number described.
GMAT assassins aren't born, they're made,
Rich
These types of questions are always carefully written, so you have to pay attention to the details and you have to think about the limitations for each digit.
For example, a 6-digit number won't start with a 0, but the other digits could be 0 (unless it's a numerical code, then it MIGHT be able to start with a 0). Here, I'll assume that the intent is to ask for a 6-digit number with no special rules to consider besides the ones that you listed....
The possible 6-digit numbers are 100,000 - 999,999, inclusive, so there are 900,000 possible numbers.
We're asked for the probability of finding a very specific type of 6-digit number
1st Digit: 1-9 = 9 possibilities
4th Digit: MUST match the 1st = 1 possibility (once we know the first digit)
2nd Digit: 0-9 = 10 possibilities
5th Digit: MUST match the 2nd = 1 possibility (once we know the second digit)
3rd Digit: 0-9 = 10 possibilities
6th Digit: MUST match the 3rd = 1 possibility (once we know the third digit)
So....(9)(10)(10)(1)(1)(1) = 900 possibilities that match the description
900/900,000 = 1/1,000 = the probability of finding the 6-digit number described.
GMAT assassins aren't born, they're made,
Rich
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Mathsbuddy
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Although the fist digit cannot be zero, the rest can.
However, the 1st, 2nd and 3rd digits are irrelevant, as we only need the probability of a match to each:
P(A) = P(1st = 4th) = 1/10
P(B) = P(2nd = 5th) = 1/10
P(C) = P(3rd = 6th) = 1/10
P(A AND B AND C) = 1/10 * 1/10 * 1/10 = 1/1000
However, the 1st, 2nd and 3rd digits are irrelevant, as we only need the probability of a match to each:
P(A) = P(1st = 4th) = 1/10
P(B) = P(2nd = 5th) = 1/10
P(C) = P(3rd = 6th) = 1/10
P(A AND B AND C) = 1/10 * 1/10 * 1/10 = 1/1000
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P(4th digit matches the 1st) = 1/10. (Of the 10 digits, only one will match the 1st.)abhasjha wrote:I want to know how can we approach questions of this type ?
What is the probablity of selecting a 6 digit number such that the fourth digit is the same as first digit , second digit is the same as fifth digit and third digit is the same as 6th digit ?
do not have the answer options available ....
can someone please tell me how to proceed with this ?
P(5th digit matches the 2nd) = 1/10. (Of the 10 digits, only one will match the 2nd.)
P(6th digit matches the 3rd) = 1/10. (Of the 10 digits, only one will match the 3rd.)
Since we want all of these probabilities to happen, we MULTIPLY the fractions:
1/10 * 1/10 * 1/10 = 1/1000.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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