A number x is selected at random from the numbers 1, 2, 3, and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of $x$ and $y$ is less than16.
Given: A number x is selected at random from the numbers 1, 2, 3, and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16.
To do: To find the probability that product of $x$ and $y$ is less than16.
Solution:
$x$ is selected from $1,\ 2,\ 3\ and\ 4$
$1,\ 2,\ 3,\ 4$
y is selected from $1,\ 4,\ 9\ and\ 16$
Let$ A=[1,\ 4,\ 9,\ 16,\ 2,\ 8,\ 18,\ 32,\ 3,\ 12,\ 27,\ 48,\ 36,\ 64]$ Which consists of elements that are product of $x$ and $y$.
Probability $( product\ of\ x\ and\ y\ is\ less\ than\ 16) = \frac {Number\ of\ outcomes\ less\ than\ 16}{Total\ number\ of\ possible\ outcomes}$
$=\frac{7}{14}$
$=\frac{1}{2}$
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