Question

An old man by dialing a 7 digit telephonic no. after having dialed first five digit suddenly forget the last two but he remembered that the last two digits were different. What is the probability that correct dialed ?

Answer 1

The required probability can be calculated by counting the number of different options for the last two digits.

Now, the first of them can be select in $10$ different ways. Once the first is fixed, the last digit can be selected from the $9$ remaining digits.

Hence, by multiplicative principle, total number of options $=10\times 9=90$.

Now, the old man must've dialed only $1$ of these possible $90$ options.

Therefore, probablity that correct dialed $=\frac{No.offavourableoutcomes}{Totalno.ofoutcomes}$

$=\frac{1}{90}$.

Hence, the required probability is $\frac{1}{90}$