Question

It is known that 25% of inhabitants of a community favour a political party A.

Answer 1

Answer:

i) $P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669$

ii) $P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317$

$P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211$

$P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669$

And replacing we got:

$P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883$

iii) $P(X$

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:

$X \sim Binom(n=20, p=0.25)$

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

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

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

$nCx=\frac{n!}{(n-x)! x!}$

Part i

We want this probability:

$P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669$

Part ii

We want this probability:

$P(X\geq 3)$

And we can use the complement rule and we have:

$P(X\geq 3) = 1-P(X$

And if we find the individual probabilites we got:

$P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317$

$P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211$

$P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669$

And replacing we got:

$P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883$

Part iii

We want this probability:

$P(X$

And replacing we got:

$P(X$