There are 6 pennies, 9 nickels, and 3 dimes in a box. Find the probability of...
a) P(2 nickels)- without replacement
b) P(1 nickel and then a dime)- with replacement
c) P(1 nickel and then 1 dime)- without replacement
d) P(1 penny and then 2 nickels)- without replacement

You have to find the answers for a, b,c, and d to get the full 50 points
Good luck

a) 4/17

b) 1/12

c) 3/34

d) 3/34

Step-by-step explanation:

a) The probability of choosing the first nickel is 9/(9 + 6 + 3) (because there are 9 nickels to choose from and a total of 9 + 6 + 3 = 18 coins to choose from) = 9/18 = 1/2. The probability of choosing the second nickel is 8/17 (because there's no replacement, we have 9 - 1 = 8 nickels remaining to choose from and 18 - 1 = 17 total coins). Multiply these together: (1/2) * (8/17) = 8/34 = 4/17

b) The probability of choosing a nickel is 9/18 (just like above) = 1/2. The probability of choosing a dime is 3/18 (because there are 3 dimes and since there IS replacement, we still have 18 total coins to choose from). Multiplying these, we get: (1/2) * (3/18) = 3/36 = 1/12

c) The probability of choosing a nickel is 9/18 = 1/2. The probability of choosing a dime after that is 3/17 (because there are 3 dimes to choose from, but since there's NO replacement, there are only 18 - 1 = 17 total coins). Multiplying these, we get: (1/2) * (3/17) = 3/34

d) The probability of choosing a penny is 6/18 (because there are 6 pennies) = 1/3. The probability of choosing a nickel next is 9/17 (because there is NO replacement, there are 18 - 1 = 17 total coins remaining). The probability of choosing a second nickel is 8/16 = 1/2 (because there are 17 - 1 = 16 total coins and 9 - 1 = 8 nickels left). Multiplying these, we get: (1/3) * (9/17) * (1/2) = 9/102 = 3/34

Hope this helps!

a) 4/17

b) 1/12

c) 3/34

d) 3/34

Step-by-step explanation:

Total: 6 + 9 + 3 = 18

a) 9/18 × 8/17

4/18

b) 9/18 × 3/18

1/12

c) 9/18 × 3/17

3/34

d) 6/18 × 9/17 × 8/16

3/34

-4

step-by-step explanation: