Respuesta :
Answer:
The P(x=45) is more that the P(x=20). Therefore x=45 successes is more likely to get.
Step-by-step explanation:
Given information: n=100 and p=1/3.
According to the binomial distribution, the probability of getting r success in n trials is
[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]
where, n is total trials, p is probability of success and q is probability of failure.
Total trials, n = 100
Probability of success, p = [tex]\frac{1}{3}[/tex]
Probability of failure, q = [tex]1-\frac{1}{3}=\frac{2}{3}[/tex]
The probability of 20 successes is
[tex]P(x=20)=^{100}C_{20}\times (\frac{1}{3})^{20}\times (\frac{2}{3})^{100-20}[/tex]
[tex]P(x=20)=\frac{100!}{20!(100-20)!}\times (\frac{1}{3})^{20}\times (\frac{2}{3})^{80}\approx 0.001257[/tex]
The probability of 45 successes is
[tex]P(x=45)=^{100}C_{45}\times (\frac{1}{3})^{45}\times (\frac{2}{3})^{100-45}[/tex]
[tex]P(x=45)=\frac{100!}{45!(100-45)!}\times (\frac{1}{3})^{45}\times (\frac{2}{3})^{55}\approx 0.004296[/tex]
The P(x=45) is more that the P(x=20). Therefore x=45 successes is more likely to get.
