There are 5 pennies, 7 nickels, and 9 dimes in an antique coin collection
two coins are to be selected at random from the collection. Find each
10. P(selecting 2 pennies), if no replacement occurs
11. P(selecting 2 pennies), if replacement occurs
12. P(selecting the same coin twice), if no replacement occurs

10. 4.8%

11. 5.67%

12. 30.39%

Step-by-step explanation:

The total number of coins is 5 + 7 + 9 = 21 coins

The probability of selecting two pennies without replacemente is:

First penny: 5 possibilities over 21 coins: 5/21

Second penny: 4 possibility over 20 coins: 4/20

P(selecting 2 pennies) = (5/21) * (4/20) = 1/21 = 0.048 = 4.8%

With replacement, we have:

First penny: 5 possibilities over 21 coins: 5/21

Second penny: 5 possibilities over 21 coins: 5/21

P(selecting 2 pennies) = (2/21) * (2/21) = 25/441 = 0.0567 = 5.67%

The cases for selecting the same coin are:

First penny: 5 possibilities over 21 coins: 5/21

Second penny: 4 possibilities over 20 coins: 4/20

P(selecting 2 pennies) = (5/21) * (4/20) = 20/420

First nickel: 7 possibilities over 21 coins: 7/21

Second nickel: 6 possibilities over 20 coins: 6/21

P(selecting 2 nickels) = (7/21) * (6/21) = 42/441

First dime: 9 possibilities over 21 coins: 9/21

Second dime: 8 possibilities over 20 coins: 8/21

P(selecting 2 dimes) = (9/21) * (8/21) = 72/441

P(selecting the same coin twice) = P(selecting 2 pennies) + P(selecting 2 nickels) + P(selecting 2 dimes) = (20+42+72)/441 = 0.3039 = 30.39%