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two different two-digit whole numbers are selected at random. what is the probability that their product is less than 200. express your answer as a common fraction. (hints: (l) there are 90 different two-digit numbers, (2) the pair {10, 11} produces the smallest product and the pair {11, 18} produces the largest product less than 200).

Respuesta :

The probability that the product of the two two-digit numbers is less than 200 is given as follows:

43/8010.

How to calculate the probability?

A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.

There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:

90 x 89 = 8010.

(the numbers have to be different)

The desired outcomes which result in a product of less than 200 are of given as follows:

  • 10 multiplied by 9 numbers, from 11 to 19.
  • 11 multiplied by 10, 12, 13, 14, 15, 16, 17, 18. (8 numbers).
  • 12 multiplied by 10, 11, 13, 14, 15, 16. (6 numbers).
  • 13 multiplied by 10, 11, 12, 14, 15 (5 numbers).
  • 14 multiplied by 10, 11, 12, 13. (4 numbers).
  • 15 multiplied by 10, 11, 12, 13. (4 numbers).
  • 16 multiplied by 10, 11, 12. (3 numbers).
  • 17 multiplied by 10, 11. (2 numbers).
  • 18 multiplied by 10, 11. (2 numbers).

Hence the number of desired outcomes is given as follows:

9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.

Meaning that the probability is of:

43/8010.

More can be learned about probabilities at https://brainly.com/question/14398287

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