Question

A bag contains 100 tickets numbered 1, 2, 3, .... 100. If a ticket is drawn out of it at random, what is the probability that the ticket drawn has the digit 2 appearing on it?

• A. \(\frac{21}{100}\)
• B. \(\frac{19}{100}\)
• C. \(\frac{32}{100}\)
• D. \(\frac{23}{100}\)

Answer 1

The Correct Option is B

To determine the probability that a ticket drawn from the bag contains the digit 2, we need to count all the ticket numbers from 1 to 100 that include the digit 2.

First, we identify these numbers:

• Single-digit numbers containing 2: 2 (1 number)
• Double-digit numbers containing 2:
  • Ten place: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 (10 numbers)
  • Unit place: 12, 32, 42, 52, 62, 72, 82, 92 (8 additional numbers, except 22 which was already counted)

Total numbers containing the digit 2: 1 (single-digit) + 10 (tens place in double-digit) + 8 (units place in double-digit) = 19 numbers.

The probability of drawing a ticket with the digit 2 is the number of favorable outcomes divided by the total number of outcomes:

\[P(\text{digit 2}) = \frac{19}{100}\]

Thus, the probability that the ticket drawn has the digit 2 on it is \(\frac{19}{100}\).