For this problem, assume the balls in the box are numbered 1 through 9, and that an experiment consists of randomly selecting 3 balls one after another without replacement.
What probability should be assigned to the event that at least one ball has an odd number?
So what we DON"T want is the case of "all even"
Let's find the prob of that.
prob of 3 all even = (4/9)(3/8)(2/7) = 1/27
So prob of at least one odd = 1 - 1/27 = 26/27
It comes to the same thing!
Each individual outcome is 1/504 (=(1/9)*(1/8)*(1/7)).
There are 4!=24 ways of picking the even numbers, so the probability of picking all even is
24/504=1/21
This is the same as Reiny's number of 2*3*4/(9*8*7), there was a transcription error at the end and became 1/27 instead.
Proceeding with Reiny's logic, the probability of picking at least one odd ball is therefore 1-1/21=20/21 (or 480/504).
It says that answer is wrong :(
the probability to each outcome is 1/504
I tried 5/504 for my question and it came out wrong
To find the probability of the event that at least one ball has an odd number, we can use the concept of complementary probability. The complementary event is the event that no ball has an odd number.
To solve this problem, follow these steps:
Step 1: Calculate the total number of possible outcomes.
Since there are 9 balls in the box, we have 9 choices for the first ball, 8 choices for the second ball (as one ball has been removed), and 7 choices for the third ball. Therefore, the total number of possible outcomes is 9 * 8 * 7.
Step 2: Calculate the number of outcomes where no ball has an odd number.
Since there are 5 even-numbered balls (2, 4, 6, 8), we have 5 choices for the first ball, 4 choices for the second ball (as one even-numbered ball has been removed), and 3 choices for the third ball. Therefore, the number of outcomes where no ball has an odd number is 5 * 4 * 3.
Step 3: Calculate the number of outcomes where at least one ball has an odd number.
Subtract the number of outcomes where no ball has an odd number from the total number of possible outcomes:
Total number of possible outcomes - Number of outcomes where no ball has an odd number
Step 4: Calculate the probability of at least one ball having an odd number.
Divide the number of outcomes where at least one ball has an odd number (from step 3) by the total number of possible outcomes (from step 1).
By following these steps, you can find the probability of the event that at least one ball has an odd number.