A box contains 9 balls marked 1 to 9. Four balls are drawn in succession
without replacement. Determine the probability that the four-digit number
formed is:
a. even
The 4-digit number is even when the last digit is even. i.e., 2,4,6, or 8.
That's 4 ways the last digit could be OUT OF 9 possible ways.
"OUT OF" means "OVER" so 4 OUT OF 9 means a probability of 4/9.
b. greater than 5000
The 4-digit number is greater than 5000 when the first digit is 5,6,7,8 or 9.
That's 5 ways the first digit could be OUT OF 9 possible ways.
"OUT OF" means "OVER" so 5 OUT OF 9 means a probability of 5/9.
c. an odd number less than 3000
To have a 'successful' 4-digit number, the 1st digit must be 1 or 2 and the 4th
digit must be 1,3,5,7 or 9.
Since the first and last digits can't both be 1, we must break the problem
down into two cases:
Case 1: The 1st digit is 1 and the last digit is 3,5,7 or 9.
That's 4 ways the 1st and 4th digits can be to have a successful number.
Case 2: The 1st digit is 2 and the last digit is 1,3,5,7,or 9.
That's 5 ways the 1st and 4th digits can be to have a successful number.
That's 4+5 or 9 ways the 1st and 4th digits can be to have a successful 4-digit
number.
There are 9∙8 or 72 ways the 1st and 4th digits can be to have either a
successful or an unsuccessful number.
That's 9 ways out of 72 or 9/72 which reduces to 1/8.
Edwin