in a population where 45%of voters prefer candidate A. an organization conducts a poll of 5 voters.Find the probability that 2 of the 5 voters will prefer Candidate.
Hey, now I have done 2. What is the probability that you can do it now?
Same old binomial distribution.
To find the probability that exactly 2 out of 5 voters prefer Candidate A, we can use the binomial probability formula.
The binomial probability formula is given by:
P(x) = ( n C x ) * ( p^x ) * ( q^(n-x) )
Where:
- P(x) is the probability of getting exactly x successes
- n is the number of trials
- x is the number of successes
- p is the probability of success in one trial
- q is the probability of failure in one trial, calculated as 1 - p
- (n C x) is the binomial coefficient, calculated as n! / (x! * (n-x)!)
In this case:
- n = 5 (number of voters in the poll)
- x = 2 (number of voters who prefer Candidate A)
- p = 0.45 (probability of one voter preferring Candidate A)
- q = 1 - p = 1 - 0.45 = 0.55 (probability of one voter not preferring Candidate A)
Now, let's calculate the probability:
P(2) = ( 5 C 2 ) * ( 0.45^2 ) * ( 0.55^(5-2) )
First, calculate the binomial coefficient:
( 5 C 2 ) = 5! / ( 2! * (5-2)! ) = (5 * 4) / (2 * 1) = 10
Next, substitute the values into the formula:
P(2) = 10 * (0.45^2) * (0.55^3)
Calculate the powers:
P(2) = 10 * 0.2025 * 0.166375
Multiply the values:
P(2) ≈ 0.03359063
So, the probability that exactly 2 out of 5 voters prefer Candidate A is approximately 0.0336, or 3.36%.