Question

use the following information to answer questions #19 - 20. in a bag there are 12 coins total. half of the coins are pennies, one - third of the coins are dimes, and the rest are quarters. you are choosing a coin, without looking, from the bag and rolling a number cube labeled 1 - 6. 19. what is the probability of choosing a penny and rolling a 2? 20. what is the probability of choosing a penny or a quarter and rolling an odd number?

Explanation:

Step1: Calculate number of pennies

There are 12 coins total. Half are pennies, so number of pennies is $\frac{12}{2}=6$.

Step2: Calculate probability of choosing a penny

Probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, favorable outcome is choosing a penny and total number of outcomes is choosing any coin. So probability of choosing a penny is $\frac{6}{12}=\frac{1}{2}$.

Step3: Probability of rolling a 2 on a number - cube

A standard number - cube has 6 faces numbered 1 - 6. The probability of rolling a 2 is $\frac{1}{6}$.

Step4: Calculate combined probability for question 19

Since choosing a coin and rolling a number - cube are independent events, the probability of both events occurring is the product of their individual probabilities. So $P=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$.

Step5: Calculate number of non - penny coins that are quarters

One - third of the coins are dimes, so number of dimes is $\frac{1}{3}\times12 = 4$. Number of pennies is 6. So number of quarters is $12-(6 + 4)=2$.

Step6: Calculate probability of choosing a penny or a quarter

Number of pennies or quarters is $6 + 2=8$. Probability of choosing a penny or a quarter is $\frac{8}{12}=\frac{2}{3}$.

Step7: Probability of rolling an odd number on a number - cube

Odd numbers on a number - cube are 1, 3, 5. So probability of rolling an odd number is $\frac{3}{6}=\frac{1}{2}$.

Step8: Calculate combined probability for question 20

Since choosing a coin and rolling a number - cube are independent events, the probability of both events occurring is the product of their individual probabilities. So $P=\frac{2}{3}\times\frac{1}{2}=\frac{1}{3}$.

Answer:

1. $\frac{1}{12}$
2. $\frac{1}{3}$