31% of a certain country\'s voters think that it is too easy to vote in their co

Question

31%

of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.

(a)

Upper P left parenthesis 3 right parenthesis equals nothingP(3)=

(Round to three decimal places as needed.)(b)

Upper P left parenthesis x greater than or equals 4 right parenthesis equals nothingP(x4)=

(Round to three decimal places as needed.)(c)

Upper P left parenthesis x less than 8 right parenthesis equals nothingP(x<8)=

(Round to three decimal places as needed.)

Explanation / Answer

a. This is an example of binomial probability with Bernoulli trials, the probability of voters who think, its easy to vote is, p=0.31 and q=1-0.31=0.69

P(exactly r)=nCr(p)^r(q)^n-r

Therefore, P(X=3)=12C3(0.31)3(0.69)^9=0.232

b. 1-P(at most 4)=1-P(X=0)+P(X=1)+...+P(X=4)=1-0.697=0.303

c. P(X<8)=P(X=0)+....+P(X=7)=0.988

In all the above cases, use the formula of nCr as n!/r!(n-r)! if your calculator do not support the function.

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