SOLUTION: A box obtains 9 balls marked 1 to 9. Four ball are drawn in succession without replacement. Determine the probability that the four-digit number formed is: A. Even B. Greater

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Question 1153828: A box obtains 9 balls marked 1 to 9. Four ball are drawn in succession without replacement. Determine the probability that the four-digit number formed is:
A. Even
B. Greater than 5000
C. An odd number less than 3000
Answer by greenestamps(13203) About Me  (Show Source):
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A. P(even)

The last ball drawn has to be even. 4 of the 9 balls are even.

P(even) = 4/9

B. P(greater than 5000)

The first ball drawn has to be 5 or greater. 5 of the 9 balls are 5 or greater.

P(greater than 5000) = 5/9

C. P(odd and less than 3000)

We have to separate this into two cases. The last ball drawn has to be odd; the first has to be either 1 or 2.

If the first ball drawn is the 1 (probability 1/9), then 4 of the remaining 8 balls are odd.

P(odd number with first digit 1) = (1/9)(4/8) = 4/72

If the first ball drawn is the 2 (also probability 1/9), then 5 of the remaining 8 balls are odd.

P(odd number with first digit 2) = (1/9)(5/8) = 5/72

P(odd number less than 3000) = 4/72+5/72 = 9/72 = 1/8