Question

A recent study suggests that 70% of all eligible voters will vote in the next presidential election. Six voters are randomly selected what is the probability that at least two voters will vote.

Answer 1

Solution

Given that ,

p = 0.70

1 - p = 1 - 0.70 = 0.30

n = 6

x = 2

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X 2) = 1 - P(X < 2)

= 1 - P(X = 0) - P(X = 1)

= 1 - ((6! / 0! (6)!) * 0.70⁰ * (0.30)⁶ - ((6! / 1! (5)!) * 0.70¹ * (0.30)⁵

= 1 - 0.0109

= 0.9891

Probability = 0.9891