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One number is chosen at random from the set {1, 2, 3, ..., 6}, and another number is chosen at random from the set {7, 8, 9, ..., 12}.  What is the probabilty that the product of the two numbers is even?

Dec 5, 2019

#1
+24344
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One number is chosen at random from the set {1, 2, 3, ..., 6},
and another number is chosen at random from the set {7, 8, 9, ..., 12}.
What is the probabilty that the product of the two numbers is even?

$$\begin{array}{|c|c|c|c|c|c|c|} \hline \text{product} & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline 1 & & even & & even& & even \\ \hline 2 & even& even& even& even& even& even \\ \hline 3 & & even & & even& & even \\ \hline 4 & even& even& even& even& even& even \\ \hline 5 & & even & & even& & even \\ \hline 6 & even& even& even& even& even& even \\ \hline \end{array}$$

The probabilty that the product of the two numbers is even is $$\dfrac{27}{36} = \mathbf{\dfrac{3}{4}}$$

Dec 5, 2019

#1
+24344
+2

One number is chosen at random from the set {1, 2, 3, ..., 6},
and another number is chosen at random from the set {7, 8, 9, ..., 12}.
What is the probabilty that the product of the two numbers is even?

$$\begin{array}{|c|c|c|c|c|c|c|} \hline \text{product} & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline 1 & & even & & even& & even \\ \hline 2 & even& even& even& even& even& even \\ \hline 3 & & even & & even& & even \\ \hline 4 & even& even& even& even& even& even \\ \hline 5 & & even & & even& & even \\ \hline 6 & even& even& even& even& even& even \\ \hline \end{array}$$

The probabilty that the product of the two numbers is even is $$\dfrac{27}{36} = \mathbf{\dfrac{3}{4}}$$

heureka Dec 5, 2019