Question

There are seven nickels and five dimes in your pocket. Three times, you randomly pick a coin out of your pocket, return it to your pocket, and then mix-up the change in your pocket. All three times, the coin is a nickel. Find the probability of this occuring.A. 343/1728B. 1/8C. 25/546D. 1/22

Answer 1

The probability of an event happening is the ratio of the number of ways it can happen to the total number of outcomes.

The total number of coins is:

`\begin{gathered} 7+5 \\ =12 \end{gathered}`

Hence, the total number of outcomes is 12.

The number of nickels is 7. Hence, the number of possible outcomes is 7.

It follows that the probability of picking a nickel each time, since the coin is always returned is:

`P(\text{nickel)}=(7)/(12)`

Since each of the events (all three), does not depend on one another, it follows that they are independent and hence, the probability of all three occurring is the product of their probabilities:

`\begin{gathered} (7)/(12)*(7)/(12)*(7)/(12) \\ =(343)/(1728) \end{gathered}`

Hence, the correct option is option A.