Respuesta :
Answer:
0.8213
Step-by-step explanation:
-This is a binomial probability problem given by the function:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}[/tex]
Given that n=21 and p=0.2, the probability that she experience a delay on at least 3 days is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 3)=1-P(X<3)\\\\=1-[P(X=0)+P(X=1)+P(X=2)]\\\\=1-[{21\choose 0}0.2^0(1-0.2)^{21}+{21\choose 1}0.2^1(1-0.2)^{20}+{21\choose 2}0.2^2(1-0.2)^{19}]\\\\=1-[0.0092+0.0484+0.1211]\\\\=0.8213[/tex]
Hence, the probability that she experience delay on at least 3 days is 0.8213
For the next 21 days that Sasha travels to work, the probability that Sasha will experience a delay due to traffic on at least 3 of the days is 0.8213.
What is binomial probability?
The binomial probabilities are the experimental probability in which the total number of output values is 2, therefore it is known as binomial probabilities.
The number of independence variable in case of binomial experiments is fixed. Both the two output has the 1/2 chances to occur. It can be given by the function,
[tex]P(X)=\left(^nC_x\right)p^xq^{n-x}[/tex]
Here, (n) is the number of trial (x) is number of successes desired, (p) is the probability of success in one trial and (q) is the probability getting a failure in one trial.
For each day that Sasha travels to work, the probability that she will experience a delay due to traffic is 0.2. Thus, probability of success is 0.2. Probability of failure is,
[tex]q=1-p\\q=1-0.2\\q=0.8[/tex]
For the next 21 days, Sasha travels to work, and experience a delay due to traffic on at least 3 of the days. For at least 3 days delay,
[tex]P(X\geq3)=1-[P(0)+P(1)+P(2)][/tex]
The number of trial is 21. Thus, by the formula,
[tex]P(X)=[1-\left(^{21}C_0\right)0.2^00.8^{21-0}+\left(^{21}C_1\right)0.2^10.8^{21-1}+\left(^{21}C_2\right)0.2^20.8^{21-2}]\\P(X)=1-[0.0092+0.0484+0.1211]\\P(X)=0.8213[/tex]
Thus, for the next 21 days that Sasha travels to work, the probability that Sasha will experience a delay due to traffic on at least 3 of the days is 0.8213.
Learn more about the binomial probability here;
https://brainly.com/question/24756209
