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Question

A number x is selected at random from the numbers $$1,2,3$$ and $$4$$. Another number y is selected at random from numbers $$1,4,9$$ and $$16$$. Find the probability that product of x and y is less than $$16$$.


Solution

 Let $$x=1\implies y<16$$
Probability of $$x{y}$$ is less than $$16$$ is $$\dfrac{3}{4^{2}}$$
Let $$x=2\implies y<8$$
Probability of $$x{y}$$ is less than $$16$$ is $$\dfrac{2}{4^{2}}$$ 
Let $$x=3\implies y<\dfrac{16}{3}$$
Probability of $$x{y}$$ is less than $$16$$ is $$\dfrac{2}{4^{2}}$$
Let $$x=4\implies y<4$$
Probability of $$x{y}$$ is less than $$16$$ is $$\dfrac{1}{4^{2}}$$
Total Probability of $$x{y}$$ is less than $$16$$ is $$\dfrac{3}{16}+\dfrac{2}{16}+\dfrac{2}{16}+\dfrac{1}{16}=\dfrac{1}{2}$$ 

Mathematics

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