Stuck on a probability question - scrambled phone number

In summary, the conversation discusses the probability of correctly guessing the first three numbers and at least one of the numbers in the last four of a phone number that has been scrambled. While the initial calculation suggests a probability of 18/3!4!, the correct answer is 15/3!4!. This can be found by considering all possible options and using properties of probability.
  • #1
fbab
1
0
The question goes like this:
Suppose a phone number is 123-4567, and that the first three numbers and last 4 numbers are scrambled.

First parts I figured out:
Probability of choosing every number correctly: 1/3!4!
probability of choosing of choosing the first 3 correctly:1/3!

Where I got stuck on, the probability of having the first three correct, and at least 1 of the numbers in the last 4 correct. My initial reaction was that it would be 1/3!* the probability of not getting any correct in the last 4. I just do not know how to calculate this, I initially thought it would be (3/4)*(2/3)*(1/2) which would be 1/4 which would have given me a final answer of 18/3!4!.

Looking at the answer in the back of the book showed me the answer was 15/3!4!. I now know this is the answer by writing down all the possible options, but would love to know how to come by this answer with properties of probability.

Any help would be greatly appreciated!
 
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  • #2
Re: Stuck on a prob question

fbab said:
The question goes like this:
Suppose a phone number is 123-4567, and that the first three numbers and last 4 numbers are scrambled.

First parts I figured out:
Probability of choosing every number correctly: 1/3!4!
probability of choosing of choosing the first 3 correctly:1/3!

Where I got stuck on, the probability of having the first three correct, and at least 1 of the numbers in the last 4 correct. My initial reaction was that it would be 1/3!* the probability of not getting any correct in the last 4. I just do not know how to calculate this, I initially thought it would be (3/4)*(2/3)*(1/2) which would be 1/4 which would have given me a final answer of 18/3!4!.

Looking at the answer in the back of the book showed me the answer was 15/3!4!. I now know this is the answer by writing down all the possible options, but would love to know how to come by this answer with properties of probability.

Any help would be greatly appreciated!
Hello fbab,
Welcome to MHB!
What is the probability that having
1xx-xxxx
x2x-xxxx
xx3-xxxx

Regards
\(\displaystyle |\rangle\)
 

FAQ: Stuck on a probability question - scrambled phone number

What is the probability of correctly guessing a scrambled phone number?

The probability of correctly guessing a scrambled phone number is extremely low, as there are over 10 billion possible combinations for a 10-digit phone number.

Is there a pattern to scrambled phone numbers that can help solve the probability question?

No, there is no pattern to scrambled phone numbers that can help solve the probability question. Each digit in a phone number is completely random and independent of the others.

Can the probability of guessing a scrambled phone number be calculated?

Yes, the probability can be calculated using the formula P(event) = # of desired outcomes / # of possible outcomes. In this case, the # of desired outcomes is 1 (correctly guessing the phone number) and the # of possible outcomes is over 10 billion.

Are there any strategies for increasing the chances of correctly guessing a scrambled phone number?

No, there are no strategies for increasing the chances of correctly guessing a scrambled phone number. It is purely a matter of luck and probability.

What is the likelihood of guessing the first 3 digits of a scrambled phone number correctly?

The likelihood of guessing the first 3 digits of a scrambled phone number correctly is slightly higher than the overall probability, as there are only 1,000 possible combinations for the first 3 digits. However, it is still a very low chance of success.

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