SOLUTION: In a binomial distribution n = 7 and p = 0.25. Find the probabilities of the following events: (Round the final answers to 3 decimal places.)
a. x = 2.
Probability:
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Question 1118075: In a binomial distribution n = 7 and p = 0.25. Find the probabilities of the following events: (Round the final answers to 3 decimal places.)
a. x = 2.
Probability:
b. x ≤ 2 (the probability that x is equal to or less than 2).
Probability:
c. x ≥ 3 (the probability that x is equal to or greater than 3).
Probability:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where the probability of succcess on any single trial is 
is given by
\ =\ {{n}\choose{k}}\(p\)^k\(1-p\)^{n-k})
The probability of the number of successes being less than or equal to in trials is:
\ =\ \sum_{i=0}^k\,{{n}\choose{i}}(p\)^i\(1-p\)^{n-i})
The probability of the number of successes being greater than or equal to in trials is:
\ =\ \sum_{i=k}^n\,{{n}\choose{i}}(p\)^i\(1-p\)^{n-i})
Note that
\ +\ P(n,\leq k-1,p)\ =\ 1)
, so for your third problem, you will have one less term to calculate if you use:
\ = 1\ -\ P(n,\leq k-1,p)\ =\ 1\ -\ \sum_{i=0}^{k-1}\,{{n}\choose{i}}(p\)^i\(1-p\)^{n-i})
Some calculation shortcuts:
John
My calculator said it, I believe it, that settles it
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