Question

In a certain congressional district, it is known that 40% of the registered voters classify themselves as conservatives. If ten registered voters are selected at random from this district, what is the probability that two of them will be conservatives? (Round your answer to four decimal places.)

Answer 1

Solution

Back-up Theory

If X ~ B(n, p). i.e., X has Binomial Distribution with parameters n and p, where n = number of trials and

p = probability of one success, then, probability mass function (pmf) of X is given by

p(x) = P(X = x) = (ⁿC_x)(p^x)(1 - p)^{n – x}, x = 0, 1, 2, ……. , n ………….............................................................………..(1)

[This probability can also be directly obtained using Excel Function: Statistical, BINOMDIST....................………….(1a)

Now, to work out the solution,

Let X = number of registered voters out of a sample 10 who classify themselves as conservatives.

Then, X ~ B(10, 0.4) .................................................................................................................................................. (2)

Probability that two of them will be conservatives

= P(X = 2)

= (¹⁰C₂)(0.4²)(0.6)⁸ [vide (1) and (2)]

= 0.1209 [vide (1a)] Answer

DONE