Respuesta :
Answer:
Probability that 3 out of the next 5 voters approving the proposal is 0.3125.
Step-by-step explanation:
We are given that the sample probability of the voters approving the proposal is 50% and Political scientists want to determine the probability of exactly 3 out of the next 5 voters they meet approving a proposal.
The above situation can be represented through binomial distribution;
[tex]P(X=r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 5
r = number of success = exactly 3
p = probability of success which in our question is probability of
the voters approving the proposal, i.e; p = 50%
Let X = Number of voters approving the proposal
So, X ~ Binom(n = 5 , p = 0.50)
Now, Probability that 3 out of the next 5 voters approving the proposal is given by = P(X = 3)
P(X = 3) = [tex]\binom{5}{3} \times 0.50^{3} \times (1-0.50)^{5-3}[/tex]
= [tex]10 \times 0.50^{3} \times 0.50^{2}[/tex]
= 0.3125
