Suppose that a poll of 18 voters is taken in a large city. The random variable x denotes the number of votes who favor a certain candidate for mayor. Suppose that 43% of all the city's voters favor the candidate. Find the probability that exactly 10 of the sampled voters favor the candidate. (round to three decimal places)

Answer: 0.105Step-by-step explanation:Binomial probability formula :-[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex], here P(X) is the probability of getting success in x trials , n is total trials and p is the probability of getting success in each trial.Given : The random variable x denotes the number of votes who favor a certain candidate for mayor.Sample size : n=18The probability that city's voters favor the candidate: p=0.43Now, the probability that exactly 10 of the sampled voters favor the candidate is given by :-[tex]P(X)=^{18}C_{10}(0.43)^{10}(1-0.43)^{8}\\\\=\dfrac{18!}{8!10!}(0.43)^{10}(0.57)^8\\\\=0.105375795236approx0.105[/tex]Hence, the probability that exactly 10 of the sampled voters favor the candidate = 0.105