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?

Answer:0.6Step-by-step explanation:Among numbers 1, 2, 3, 4, 5 and 6, the square numbers are 1 and 4.The probability that both of these two cards do not show a square number (both selected cards show numbers 2 or 3 or 5 or 6) is[tex]Pr=\dfrac{C_4^2}{C_6^2}=\dfrac{\frac{4!}{2!(4-2)!}}{\frac{6!}{2!(6-2)!}}=\dfrac{4!\cdot 2!\cdot 4!}{2!\cdot 2!\cdot 6!}=\dfrac{1\cdot 2\cdot 3\cdot 4}{1\cdot 2\cdot 5\cdot 6}=\dfrac{2}{5}.[/tex]The probability that at least one of those two cards shows a square number is[tex]1-Pr=1-\dfrac{2}{5}=\dfrac{3}{5}=0.6.[/tex]