Question #339504

It has been reported that 70% of university students do volunteer work during their summer vacation. Four students are randomly selected to do volunteer work.


a. The probability that at least 1 student will do volunteer work this summer (correct to 3 decimal places) is 


b. The probability that exactly 3 graduates will not do any volunteer work this summer (correct to 4 decimal places) is 


c. The expected number of students (correct to 1 decimal place) who will not do volunteer work this summer is


1
Expert's answer
2022-05-11T12:46:06-0400

Let X=X= the number of students who do volunteer work during their summer vacation:XBin(n,p).X\sim Bin(n, p).

Given n=4,p=0.7,q=1p=0.3.n=4, p=0.7, q=1-p=0.3.

a.


P(X1)=1P(X=0)P(X\ge1)=1-P(X=0)

=1(40)(0.7)0(0.3)40=0.992=1-\dbinom{4}{0}(0.7)^0(0.3)^{4-0}=0.992

b.


P(XC=3)=P(X=1)=(41)(0.7)1(0.3)41P(X^C=3)=P(X=1)=\dbinom{4}{1}(0.7)^1(0.3)^{4-1}

=0.0756=0.0756

c.

E(XC)=nq=4(0.3)=1.2E(X^C)=nq=4(0.3)=1.2



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