Question

2. 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 at least one of the five would strongly support the proposal?

Answer 1

n = 5

p = 0.25

$P(X=x) = C^n_xp^x(1-p)^{n-x}$

Compute the probability that at least one of the five senators will support the tax proposal.

$P(X≥1) = 1 - P(X<1) \\ = 1 - P(X=0) \\ = 1 - (C^5_0 \times 0.25^0 \times 0.75^{5}) \\ = 1 -0.2373 \\ = 0.7627$

The probability that at least one of the five senators will support the tax proposal is 0.7627.