A)
The probabilities in the first column are:
19/32; 6/32; 7/32
The probabilities in the second column are:
18/31; 6/31; 7/31; 19/31; 5/31; 7/31; 19/31; 6/31; 6/31.
B)
There are 9 ways to select two coins.
There are 4 ways to select exactly one nickel.
The probability of two pennies is 171/496.
The probability of a dime then a penny is 133/992.
Explanation:
A)
There are 19 pennies out of 32 coins; 6 nickels out of 32 coins; and 7 dimes out of 32 coins.
After selecting a penny, there are 18 pennies out of 31 coins; 6 nickels out of 31 coins; and 7 dimes out of 31 coins.
After selecting a nickel, there are 19 pennies out of 31 coins; 5 nickels out of 31 coins; and 7 dimes out of 31 coins.
After selecting a dime, there are 19 pennies out of 31 coins; 6 nickels out of 31 coins; and 6 dimes out of 31 coins.
B)
Counting the outcomes in the tree, there are 9 ways of selecting two coins.
Counting the outcomes that have only one nickel, there are 4.
The probability of two pennies is 19/32(18/31) = 342/992 = 171/496
The probability of a dime then a penny is 7/32(19/31) = 133/992
