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# Probability: Binomial distribution watch

1. "A box has 3 white balls, 2 red balls, and 3 black balls. 4 balls are randomly taken out and then put back in the box. Find the probability that none of them are red".

I thought I could use the formula for binomial distribution, .

So I let: success=the ball taken out is red
(number of successes)
(number of experiments)
(probability of a success)

And so I got which apparently is wrong, I have here that the correct answer should be ?

Where have I gone wrong? Thanks!
2. (Original post by Miss Mary)
...
You don't really need the full might of the binomial, but doing it that way you are interested in 4 successes, not 0, since you've taken a success to mean "it's not red".
3. (Original post by Miss Mary)
"A box has 3 white balls, 2 red balls, and 3 black balls. 4 balls are randomly taken out and then put back in the box. Find the probability that none of them are red".

I thought I could use the formula for binomial distribution, .

So I let: success=the ball taken out is red
(number of successes)
(number of experiments)
(probability of a success)

And so I got which apparently is wrong, I have here that the correct answer should be ?

Where have I gone wrong? Thanks!

You seem to have your probability mixed up - check what's success and what's failure.
4. Ohhh yes you are right, it should be .

Thank you guys

PS: ghostwalker, just out of interest, what other method do you suggest?
5. (Original post by Miss Mary)
PS: ghostwalker, just out of interest, what other method do you suggest?
You have 4 independent events, each with a probability of 6/8, hence (6/8)^4 is the desired probabilty.

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