Question 1180971: using the bionomial distribution find probabilities ??
3 success in 8 trails when p=0.4
2 failure in 6 trails when p=0.6
2 of fewer success in 9 trails when p=0.4
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
The calculation for binomial probability is well defined; you simply need to do the calculations. You can do that as easily as we can.
I will outline the calculation required for the first problem and leave the actual work for the rest of the problem to you.
(1) 3 successes in 8 trials with p=0.4....
(a) You need to choose 3 of the 8 trials to be the successful ones: C(8,3)
(b) The probability of each of the 3 successes is 0.4: (0.4)^3
(c) The probability of each of the 5 failures is 1-0.4=0.6: (0.6)^5
ANSWER: (C(8,3))*((0.4)^3)*((0.6)^5))
Use a calculator....
The same calculation with different numbers is required for the other two problems.
(2) 2 failures in 6 trials with p=0.6....
Two notes about this one.
(a) 2 failures in 6 trials means 4 successes.
(b) The p=0.6 must be assumed to be the probability of a success
(3) 2 or fewer successes in 9 trials with p=0.4
For this one you will need to do the calculation 3 times -- with 0, 1, or 2 successes -- and add the three probabilities.
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