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# help

0
105
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Mary has six cards whose front sides show the numbers  1,2,3,4,5and 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?

Jan 16, 2019

#3
+99585
+2

P( at least one card is a square number)  =

1 - P(neither card is a square number)  =

1 - (4/6) (3/5)  =

1 - 12 /30   =

18 / 30 =   3 / 5

Jan 16, 2019

#1
+100235
+4

Mary has six cards whose front sides show the numbers  1,2,3,4,5and 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?

The only square numbers are 1 and 4

P(one of them is 4) = $$\frac{1}{6}\times \frac{5}{5}+\frac{5}{6}\times \frac{1}{5}=\frac{2}{6}$$

P(one of them is 1) = $$\frac{2}{6}$$

P(one is 1 and the other is 4)=$$2*\frac{1}{6}\times\frac{1}{5}=\frac{2}{30}$$

so

P(at least one is either a 1 or  a 4 is) =  $$\frac{4}{6}-\frac{2}{30}=\frac{18}{30}=\frac{3}{5}$$

.
Jan 16, 2019
#2
+21984
+7

Mary has six cards whose front sides show the numbers  1,2,3,4,5and 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?

$$\color{red}\text{square number}$$

$$\begin{array}{|r|r|r|r|r|r|r|r|} \hline & \text{card 2} & {\color{red}1} & 2 & 3 & {\color{red}4} & 5 & 6 \\ \hline \text{card 1} & & & & & & & \\ \hline {\color{red}1} & & - & \times & \times & \times & \times & \times \\ \hline 2 & & \times & - & & \times & & \\ \hline 3 & & \times & & - & \times & & \\ \hline {\color{red}4} & & \times & \times & \times & - & \times & \times \\ \hline 5 & & \times & & & \times & - & \\ \hline 6 & & \times & & & \times & & - \\ \hline \end{array}$$

$$\text{The probability is \dfrac{18}{30} = \dfrac{3}{5} \quad (60\ \%)  }$$

Jan 16, 2019
edited by heureka  Jan 16, 2019
#3
+99585
+2

P( at least one card is a square number)  =

1 - P(neither card is a square number)  =

1 - (4/6) (3/5)  =

1 - 12 /30   =

18 / 30 =   3 / 5

CPhill Jan 16, 2019
#4
+100235
+1

I like CPhill's answer best but they are all correct.

Jan 16, 2019