Question

1. a pocket contains 3 pennies, 2 nickels, 3 quarters and 4 dimes. what is the probability of randomly choosing a quarter two times in a row if the first coin drawn is not replaced?

Explanation:

Step1: Calculate total number of coins

First, we find the total number of coins by adding the number of each type of coin. There are 3 pennies, 2 nickels, 3 quarters, and 4 dimes. So the total number of coins \( n = 3 + 2 + 3 + 4 = 12 \).

Step2: Probability of first quarter

The number of quarters is 3. So the probability of drawing a quarter first, \( P_1=\frac{3}{12}=\frac{1}{4} \).

Step3: Probability of second quarter (without replacement)

After drawing one quarter, the number of quarters left is \( 3 - 1 = 2 \), and the total number of coins left is \( 12 - 1 = 11 \). So the probability of drawing a quarter second, \( P_2=\frac{2}{11} \).

Step4: Probability of both events

Since the two events (drawing a quarter first and then a quarter second) are dependent, we multiply the probabilities: \( P = P_1\times P_2=\frac{1}{4}\times\frac{2}{11}=\frac{2}{44}=\frac{1}{22} \).

Answer:

\(\frac{1}{22}\)