Tickets numbered 11 to 3030 are mixed up and a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of both 22 and 33?. Give the answer accurate to two decimal places.

To find the probability that the ticket has a number which is a multiple of both 22 and 33, we need to determine the total number of tickets that satisfy this condition and divide it by the total number of tickets.

Step 1: Find the multiples of 22 and 33 within the given range. The multiples of 22 within the range are: 22, 44, 66, ..., 3030. The multiples of 33 within the range are: 33, 66, 99, ..., 3030.

Step 2: Find the common multiples of 22 and 33 within the given range. The common multiples of 22 and 33 within the range are: 66, 132, 198, ..., 3030.

Step 3: Determine the total number of tickets that satisfy the condition. To find the total number of tickets, we need to count the number of common multiples of 22 and 33 within the range. In this case, the last common multiple is 3030.

Step 4: Calculate the probability. The probability is given by the number of favorable outcomes (common multiples of 22 and 33) divided by the total number of outcomes (total number of tickets).

Number of favorable outcomes = Number of common multiples of 22 and 33 = 3030 / 66 = 46.09 (rounded to two decimal places)

Total number of outcomes = Total number of tickets = 3030 - 11 + 1 = 3020

Probability = Number of favorable outcomes / Total number of outcomes = 46.09 / 3020 = 0.015 (rounded to two decimal places)

Therefore, the probability that the ticket has a number which is a multiple of both 22 and 33 is 0.015.