Question

Find the probability. There are six nickels and seven dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Then you randomly pick another coin. Both times the coin is a nickel.a. 6/13b. 2/7c. 5/16d. 3/19

Answer 1

Answer:

$\frac{6}{13}\cdot \frac{6}{13}$

Step-by-step explanation:

We have been given that there are six nickels and seven dimes in your pocket. We are asked to find the probability of getting a nickel coin both times with replacement.

Let us find probability of getting a nickel in one pick.

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

There are 6 nickels and total coins are 6 nickels plus 7 dimes that 13 coins.

$P(\text{Nickel})=\frac{6}{13}$

Since the coin is returned back in the pocket, so probability of choosing 2nd nickel will be $\frac{6}{13}$.

Since both terms are independent, therefore, probability the required probability will be product of $\frac{6}{13}$ and $\frac{6}{13}$.

$P(\text{Getting two nickels})=\frac{6}{13}\cdot \frac{6}{13}$

Therefore, our required probability would be $\frac{6}{13}\cdot \frac{6}{13}$.