# Conditional probability problem

• MathMan2022
In summary, 0.23 of the population is said to for a certain political block A at an election. 10 people are sampled.

#### MathMan2022

Homework Statement
45% of the population is said to for a certain political block A at an election. 10 people are sampled.

a) Whats the prob that 5 of them vote block A?

b) What the prob that none of them vote block A?
Relevant Equations
P(A and B) = P(A) * P(B)
P(Not B) = 1 - P(B)
A) P(A and B) = 0.45 * 5/10
B P(Not B) = 1 - ( 0.45 * 5/10)

Is it like this?

MathMan2022 said:
Homework Statement:: 45% of the population is said to for a certain political block A at an election. 10 people are sampled.

a) Whats the prob that 5 of them vote block A?

b) What the prob that none of them vote block A?
Relevant Equations:: P(A and B) = P(A) * P(B)
P(Not B) = 1 - P(B)

A) P(A and B) = 0.45 * 5/10
B P(Not B) = 1 - ( 0.45 * 5/10)

Is it like this?
It's nothing like that. What have you learned about probability theory so far? Have you heard the term binomial coefficients?

PeroK said:
It's nothing like that. What have you learned about probability theory so far? Have you heard the term binomial coefficients?
Oh its like that? Yes I have heard of that.

P(X = r) = K(n,r)*p^r*(1-p)^(n-r) right?

So
a) P(X = 5) = K(10, 5)*0.45^5*(1 - 0.45)^(10 - 5)= 0.23
b) P(X = no votes) = 1- P(X=5) = 1-0.23

MathMan2022 said:
So
a) P(X = 5) = K(10, 5)*0.45^5*(1 - 0.45)^(10 - 5)= 0.23
That looks a lot better.
MathMan2022 said:
b) P(X = no votes) = 1- P(X=5) = 1-0.23
Why would no votes be the complement of 5 votes? That's the probability of any number of votes except 5.

If 45% is sampled to vote for block A. Then 55 % must non voters for block A?

MathMan2022 said:
If 45% is sampled to vote for block A. Then 55 % must non voters for block A?
No, it means that 55% don't vote for block A.

MathMan2022 said:
If 45% is sampled to vote for block A. Then 55 % must non voters for block A?
Look at it this way, suppose you change part a) to calculate ##P(X = 4)##. Would your answer to part b) change to ##P(X = 0) = 1 - P(X = 4)##?

PeroK said:
Look at it this way, suppose you change part a) to calculate ##P(X = 4)##. Would your answer to part b) change to ##1 - P(X = 4)##?
That would that is the prob that 4 people or less voted for block A?

MathMan2022 said:
That would that is the prob that 4 people or less voted for block A?
No, that would be the probablity that 0, 1, 2, 3, 5, 6, 7, 8, 9 or 10 people vote for block A. Any number but ##4##. Note that we have:
$$\sum_{n = 0}^{10} P(X = n) = 1$$

PeroK said:
No, that would be the probablity that 0, 1, 2, 3, 5, 6, 7, 8, 9 or 10 people vote for block A. Any number but ##4##. Note that we have:
$$\sum_{n = 0}^{10} P(X = n) = 1$$
Then that would be P(X=0) I am searching for? Because that would be the prob that non of the 10 voted for block A.

PeroK
MathMan2022 said:
Then that would be P(X=0) I am searching for? Because that would be the prob that non of the 10 voted for block A.
Yes, exactly.

MathMan2022
Here's a tip. The Excel spreadsheet has a binomial distribution function (and other useful statistical things). For example, if you type:

=BINOMDIST(5, 10, 0.45, FALSE)

Then, you'll get the answer ##0.23##.