Question 934490
For each adult in the random sample, the probability that he/she contributes to charitable agencies on a regular basis is
{{{160/1000=0.16}}} ,
and the probability that he/she does not contribute to charitable agencies on a regular basis is
{{{1-0.16=0.84}}} .
The probability that exactly 5 of the 12 randomly selected contribute to charitable agencies on a regular is represented by the term in the binomial expansion of
{{{(0.16+0.84)^12}}}
that has {{{0.16^5}}} .
The coefficient of that term is {{{12*11*10*9*8/(1*2*3*4*5)=792}}} .
The term is
{{{792*0.16^5*0.84^7=0.0245}}} (rounded).