Question

 A politician believes that 25% of all macroeconomists in senior positions would strongly support a proposal he wishes to advance. Suppose that this belief is correct and that five senior macroeconomists are approached at random. What is the probability that all 5 will strongly support the proposal?

Answer 1

$n = 5\\ p = 0.25$

$P(X=x) = \binom{n}{x}p^x(1-p)^{n-x}$

We shall compute the probability that all five macroeconomists will support the proposal.

$p(X=5)= \binom{5}{5}\times 0.25^5 \times 0.75^{0}=0.25^5 = 0.001$

Therefore, the probability that all the five senior macroeconomists will support the proposal is 0.001