MHB What is the Probability of Selecting at Least One Odd Numbered Ball?

[elimeli]

The final question in my homework says:

Assume the balls in the box are numbered 1 through 8, 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?

I have tried several approaches to the problem but they are all wrong :( Can somebody explain how to solve this?

 

[Greg]

Hi elimeli. Are you willing to post your work and indicate where you may have had errors/misunderstandings?

 

[elimeli]

Hi elimeli. Are you willing to post your work and indicate where you may have had errors/misunderstandings?

Since there are 336 outcomes, which I got by multiplying 8 x 7 x 6, that means that each outcome is assigned a probability of 1/336. Since they were asking for balls with odd numbers, I "removed" the even numbers from the original set of outcomes, so that it would be 4 x 3 x 2. So I assumed that at least one odd ball would be 4 x 3 x 2/8 x 7 x 6. However, that was not the answer. My other assumptions were guesses.

 

[I like Serena]

Since there are 336 outcomes, which I got by multiplying 8 x 7 x 6, that means that each outcome is assigned a probability of 1/336. Since they were asking for balls with odd numbers, I "removed" the even numbers from the original set of outcomes, so that it would be 4 x 3 x 2. So I assumed that at least one odd ball would be 4 x 3 x 2/8 x 7 x 6. However, that was not the answer. My other assumptions were guesses.

Hi elimeli,

You've found the probability to find only even balls.
The probability to find at least one odd ball is the complement.
That is:
$$P(\text{at least one odd}) = 1 - P(\text{only even}) = 1 - \frac{\text{# combinations with only even}}{\text{# total}} = 1 - \frac{4 \cdot 3 \cdot 2}{8 \cdot 7 \cdot 6}$$