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The last three digits of a telephone number have been erased and all we know is that the number was 25785???. Assuming that all possibilities are equally likely, the probability that the missing digits are all equal to each other is
  • a)
    0.001
  • b)
    0.006
  • c)
    0.010
  • d)
    0.270
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The last three digits of a telephone number have been erased and all w...
000, 111, ....999
there are 10 cases in our favour out of 10 x 10 x 10 possible case, So, probability is
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The last three digits of a telephone number have been erased and all w...
Given:
The last three digits of a telephone number have been erased and all we know is that the number was 25785???.

To find:
The probability that the missing digits are all equal to each other.

Solution:
To determine the probability, we need to find the number of favorable outcomes (where the missing digits are all equal) and divide it by the total number of possible outcomes.

Total Number of Possible Outcomes:
The last three digits can take any value from 0 to 9, so there are 10 possibilities for each digit. Since there are three digits, the total number of possible outcomes is 10^3 = 1000.

Favorable Outcomes:
To have all three missing digits equal, we need to choose one digit from 0 to 9 as the missing digit. Once a digit is chosen, there is only one possibility for the remaining two digits to be equal to the chosen digit. Therefore, there are 10 possible choices for the missing digit.

Probability:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 10 / 1000
Probability = 0.01

Therefore, the probability that the missing digits are all equal to each other is 0.01, which is option 'c'.
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The last three digits of a telephone number have been erased and all we know is that the number was 25785???. Assuming that all possibilities are equally likely, the probability that the missing digits are all equal to each other isa)0.001b)0.006c)0.010d)0.270Correct answer is option 'C'. Can you explain this answer?
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