Alright, let's solve this step-by-step.
1. Identify the total number of coins:
Jeanette has 3 quarters and 6 dimes in her hand. To find the total number of coins, we add the number of quarters to the number of dimes.
[tex]\[
\text{Total number of coins} = \text{Number of quarters} + \text{Number of dimes} = 3 + 6 = 9
\][/tex]
2. Calculate the probability of dropping a dime:
The probability of an event happening is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, the favorable outcome is dropping a dime. There are 6 dimes available.
[tex]\[
\text{Probability of dropping a dime} = \frac{\text{Number of dimes}}{\text{Total number of coins}} = \frac{6}{9}
\][/tex]
3. Simplify the fraction:
We can simplify [tex]\(\frac{6}{9}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
[tex]\[
\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\][/tex]
Therefore, the probability that Jeanette drops a dime is [tex]\(\frac{2}{3}\)[/tex].
So, the correct answer is [tex]\(\frac{2}{3}\)[/tex].
