Question

Mary has six cards whose front sides show the numbers $1,2,3,4,5,$ and $6$. She turns the cards face-down, shuffles the cards until their order is random, then pulls the top two cards off the deck. What is the probability that at least one of those two cards shows a square number? Explain your solution. Is the answer the same as in part (

a., or is it different? Why? Your Response

Answer 1

3/5

Explanation:

There are 6 possibilities for the number on the first card Mary draws. After this, there are 5 possibilities for the second card, because Mary can't draw the first card again. Thus, there are 6(5)=30 possibilities for the pair of cards.

Among these, there are 4(3) = 12 pairs that don't include at least one square number. To see why, consider that there are 4 choices for the first non-square number, then 3 choices for the second non-square number (since $1$ of the original $4$ choices has been used up).

Since 12 possible pairs don't include at least one square, the other 30-12=18 pairs do include at least one square. Therefore, the probability that Mary gets at least one square number is 18/30=3/5.

Answer 2

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