twelve jurors are randomly selected from a population of 4 million residents. Of these four million residents it is known that 47% are of a minority race. Of the 12 jurors selected 2 are minority. if 12 jurors are randomly selected from a population where 47% are minorities what is the probability that two or fewer jurors will be minorities?
Distribution: Binomial
Let the binomial random variable, X =number of successes (i.e., number of jurors who are minorities).
Let the probability =P
Sample size, n =12
Proportion of success, p =47% =0.47
Proportion of failure, q =1 - p =0.53
Formula: P(X =r) =C(n, r).pr.qn-r
The probability that two or fewer jurors will be minorities =P(X 2) =P(X =0)+P(X =1)+P(X =2) =0.0312
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