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Sagot :
An urn contains balls numbered from 1 through 20
The formula for probability is
[tex]\text{Probability}=\frac{\operatorname{Re}quired\text{ outcome}}{Total\text{ outcome}}[/tex]Where the total outcome = 20
Since, the first ball was replaced after chosen, then the two events are independent of each other
Let the probability that a first ball is taken be represents by P(F)
Let the probability that a second ball is taken be represents by P(S)
The probability that a first ball is chosen with replacement is
[tex]\begin{gathered} P(F)=\frac{1}{20} \\ \text{For a ball picked, required outcome is 1} \end{gathered}[/tex]Since there is a replacement, the probability that a second ball is chosen and will be 8 is
[tex]\begin{gathered} P(S)=\frac{1}{20} \\ \text{Note: only a ball is numbered as 8 so the required outcome is 1} \\ \end{gathered}[/tex]Probability that a first ball is chosen and a second ball is chosen is
[tex]P=P(F)\times P(S)=\frac{1}{20}\times\frac{1}{20}=\frac{1}{400}[/tex]Hence, answer is D
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