An Integer from 299 through 1,000, both inclusive, is to be chosen at random. What is the probabilit

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14 Nov 2019 Probability

An Integer from 299 through 1,000, both inclusive, is to be chosen at random. What is the probability that the number chosen will have 2 as at least one of its digit?

OPtion

1) 71/351
2) 73/351
3) 69/351
4) 70/351
5) 72/351
6) 66/351
7) 68/351
8) 67/351
9) 74/351
10) None of these

Solution

Total number of possible numbers between 1000 and 299 = 1000-298 = 702

Lets try to find count of numbers which will have 2.

1. First count of number which will have only one 2

a. Count of numbers with 2 at hundred place =
Fixing 2 at hundred place we have count of = 1
b. Count of numbers with 2 at ten's place =
Fixing 2 at ten's place we have count of = 7*1*9 = 63
c. Count of numbers with 2 at unit's place =
Fixing 2 at unit's place we have count of = 7*9*1 = 63

2. Next lets count numbers which will have exactly 2 two's
7*1*1 = 7



Total Count = 1+63+63+7 = 134

Probability = 134/702 = 67/351

Correct Option: 8 Best Solution (0)