Multiple choice

Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5?

  1. 1/6

  2. 1/5

  3. 1/3

  4. 2/5

  5. 2/3
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D Correct answer
Explanation

The total outcomes for two draws are 6 * 6 = 36. The pairs that sum to 8 are (2,6), (3,5), (4,4), (5,3), (6,2). There are 5 such outcomes. Among these, the outcomes containing a 5 are (3,5) and (5,3). The probability is 2/5.

AI explanation

Using the fundamental principle of counting, the sample space of drawing two cards with replacement and getting a sum of 8 includes the pairs (2, 6), (3, 5), (4, 4), (5, 3) and (6, 2), giving 5 total outcomes. Out of these, the pairs (3, 5) and (5, 3) include the number 5, resulting in 2 favorable outcomes. Using the classical definition of probability, we divide the favorable outcomes by the total outcomes to get 2 divided by 5.

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