Select the correct answer.
Kevin has an equal number of dimes, nickels, and quarters in his piggy bank. He randomly picks a coin, replaces it, and picks another coin. What is the probability that the sum of the two coins picked is at least 30 cents?
A.

B.

C.

D.

E.

1/3

Step-by-step explanation:

The only ways to get at least 30 cents from two coins are:

- 1 nickel (5 cents) + 1 quarter (25 cents)   -   case 1

- 1 dime (10 cents) + 1 quarter (25 cents)   -   case 2

- 1 quarter (25 cents) + 1 quarter (25 cents)   -   case 3

Case 1:

The probability of choosing a nickel is 1/3 and the probability of choosing a quarter next is also 1/3. Multiply these together:

(1/3) * (1/3) = 1/9

Case 2:

The probability of choosing a dime is 1/3 and the probability of choosing a quarter next is also 1/3. Multiply these together:

(1/3) * (1/3) = 1/9

Case 3:

The probability of choosing a quarter is 1/3 and the probability of choosing another quarter next is also 1/3. Multiply these together:

(1/3) * (1/3) = 1/9

Finally, add up these probabilities:

1/9 + 1/9 + 1/9 = 3/9 = 1/3

5/9

Step-by-step explanation:

Sum atleast 30 when:

Nickel and quarter

Quarter and nickel

Dime and quarter

Quarter and dime

Quarter and quarter

Total possibilities: 3×3 = 9

Probability = 5/9