A bag contains cards which is numbered 22 to 9090. A card is drawn at random from the bag. Find the probability that it bears a two digit even multiple of 55.

Sure, let's solve this step by step.

Step 1: Identify the range of numbers The numbers on the cards range from 22 to 9090.

Step 2: Identify the two-digit multiples of 55 The two-digit multiples of 55 are 55 and 110.

Step 3: Identify the even multiples among them Both 55 and 110 are multiples of 55, but only 110 is even.

Step 4: Calculate the total number of cards The total number of cards is 9090 - 22 + 1 = 9069.

Step 5: Calculate the probability The probability of drawing a card with a two-digit even multiple of 55 is the number of favorable outcomes divided by the total number of outcomes. In this case, there is only 1 favorable outcome (the card with the number 110), and the total number of outcomes is 9069. So, the probability is 1/9069.