It is known that 25% of inhabitants of a community favour a political party A. A random sample of 20 inhabitants was selected from the community and each person was asked he/she will vote for party A in an impending election. This follows a Binomial distribution, what is the probability that:
(i) exactly two persons will vote for party A?
(ii) at least three persons will vote for party A?
(iii) fewer than two persons will vote for party A?

i)

ii)

And replacing we got:

iii)

Step-by-step explanation:

Let X the random variable of interest "number of inhabitants of a community favour a political party', on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

Part i

We want this probability:

Part ii

We want this probability:

And we can use the complement rule and we have:

And if we find the individual probabilites we got:

And replacing we got:

Part iii

We want this probability:

And replacing we got:

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.