Forgot the number. Help!!!

Probability Level 3

Dialing a telephone number, a man forgot the last two digits and remembering only that they are different, dialed them at random.The probability of the number being dialed correctly is


The answer is 0.0111.

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

Tony Sprinkle
Jan 6, 2015

However long the phone number is, only the last two digits are being picked at random. With the constraint that both digits are different, there are 10 10 possible choices for the first digit and 9 9 possible choices for the second digit for a total of 10 × 9 = 90 10 \times 9 = 90 possibilities. Only one of those possibilities is correct, giving a probability of: 1 90 = 0.0 1 ˉ \frac{1}{90} = \boxed{0.0\bar{1}}

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i want to ask a small doubt. Whats wrong in answer being 1/2. its clear that the number will be either correct or wrong. as we want coorect answer so 1/2.. plz reply and explain

Tanishq Varshney - 6 years, 5 months ago

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We have to count all the separate ways that the number can be wrong. There are 100 2-digit combinations, but only 90 of them have distinct digits. Only 1 of those 90 2-digit combinations is correct, the other 89 are wrong. Thus, there is a 1 in 90 chance of getting the right 2 digits and, conversely, a 89 in 90 chance of getting it wrong.

Tony Sprinkle - 6 years, 5 months ago

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