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Binomial distributionBinomial distribution is a discrete distribution, and is used for situations where individual trials, experiments, or tests have only two possible outcomes such as success/failure, go/no-go, defectetive/non-defective or
pass/fail.
rNr pprNr
NpNr
)1(
)!(!
!),/(p
N is the sample size ( in a trial)
r is the number of events of interest observed in the sample (i.e. failures, or defectives)
p is the proportion of events of interest in the population
p(r / N, p) also can be written as
P (r, N, p) not to be confused with p.
Binomial Distribution - Examples
Now I look at using the formula in solving the following questions.
Q.(1)The manufacturer of a bag of sweets claims that there is a 90% chance that the bag contains some toffees. If 20 bags are chosen. What is the probability that
(i) all the bags contain toffees(ii) more than 18 bags contain toffees
Q.(2) In clinical trials a certain drug has an 8% success rate of curing a known disease. If 15 people are known to have the disease. What is the probability of at least 2 being cured.