Question

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. question #19. what is the probability of choosing a penny and rolling a 2? question #20. what is the probability of choosing a penny or a quarter and rolling an odd number?

Explanation:

Step1: Calculate number of pennies

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

Step2: Calculate probability of choosing a penny (Question 19)

Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So probability of choosing a penny is $\frac{6}{12}=\frac{1}{2}$.

Step3: Calculate number of dimes and quarters

One - third of 12 is $\frac{12}{3} = 4$ (dimes). Number of quarters is $12-(6 + 4)=2$.

Step4: Calculate probability for Question 20

Probability of choosing a penny or a quarter: There are 6 pennies and 2 quarters. So total favorable outcomes is $6 + 2=8$. Probability is $\frac{8}{12}=\frac{2}{3}$. Probability of rolling an odd number on a 1 - 6 cube is $\frac{3}{6}=\frac{1}{2}$. Since these are independent events, we use the multiplication rule for independent events $P(A\cap B)=P(A)\times P(B)$. So probability of choosing a penny or a quarter and rolling an odd number is $\frac{2}{3}\times\frac{1}{2}=\frac{1}{3}$.

Answer:

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