Answer:
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!
