Expert: Ahmed Salami - 7/7/2004

Question
Here is the question, Any help would be great

2 of 6 people who apply for a college program are accepted. If 10 people apply, what is the probability that at least 6 of them will be accepted?

Answer
Hi Travis,
This is a binomial probability question.
The binomial probability distribution describes experiments with repeated, identical trials. Each trial can have only two possible outcomes: 'Hit' or 'Fail'. The probability for 'hit', p, and the probability for 'fail', q,is the same for all trials. The number of trials, N, is fixed. The probability of observing n hits is given by
NCn (read "N combination n").(p^n)(q^N-n)
For this question, p = 2/6 = 1/3
q = 1 - 1/3 = 2/3
Therefore, for at least 6 hits, you would perform the calculations for n = 6,7,8,9,10 and add the results.
I believe you should get about 0.07624429327699411
Get back to me for any other thing.
Regards.