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A and B play a game where each is asked to select a number from 1 to 25 . If the two numbers match, both will win a prize. The probability that they will NOT win a prize in a single trial is

Options

  1. A1 25
  2. B2 25
  3. C24 25
  4. D1 25

Correct answer

C. 24 25

Step-by-step solution

The total number of possible outcomes when A and B each select a number from 1 to 25 is 25 25 = 625 . The number of favorable outcomes where they select the same number is 25, which are (1,1), (2,2), ..., (25,25). The probability that they win a prize is P( win ) = 25 625 = 1 25 . The probability that they will NOT win a prize is P( not win ) = 1 - P( win ) = 1 - 1 25 = 24 25 . Answer: 24 25

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