Question

An urn contains balls numbered 1 through 20. A ball is chosen, returned to the urn, and a second ball is chosen. What is the probability that the first and second balls will be a 8?A. 1/40B. 1/10C. 1/20D. 1/400

Answer 1

An urn contains balls numbered from 1 through 20

The formula for probability is

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

`\begin{gathered} P(F)=(1)/(20) \\ \text{For a ball picked, required outcome is 1} \end{gathered}`

Since there is a replacement, the probability that a second ball is chosen and will be 8 is

`\begin{gathered} P(S)=(1)/(20) \\ \text{Note: only a ball is numbered as 8 so the required outcome is 1} \\ \end{gathered}`

Probability that a first ball is chosen and a second ball is chosen is

`P=P(F)* P(S)=(1)/(20)*(1)/(20)=(1)/(400)`

Hence, answer is D