Respuesta :
Answer:
The required probability of none of flights will be canceled is 0.90438
The probability that exactly one will be cancelled is 0.09135
The probability that no more than one of the flights will be canceled is 0.99573
Step-by-step explanation:
Consider the provided information.
Approximately 1% of all flights sched- uled to depart from US airports are canceled
A flight is cancelled (p) = 0.01
A flight is not cancelled (q) = 1-0.01 = 0.99
You select 10 flights at random.
According to the Binomial distribution: [tex]P(X) = ^nC_x p^x q^{n-x}[/tex]
Part a. none of the flights will be canceled.
[tex]P(X=0)=^{10}C_0 (0.01)^0 (0.99)^{10}=0.90438[/tex]
Hence, the required probability of none of flights will be canceled is 0.90438
Part b. exactly one of the flights will be canceled.
[tex]P(X=1) = ^{10}C_1 (0.01)^1 (0.99)^{9}=0.09135[/tex]
Hence, the probability that exactly one will be cancelled is 0.09135
Part c. no more than one of the flights will be canceled.
[tex]P(X\leq 1) = P(X=0)+P(X=1)\\P(X\leq 1)=0.90438+0.09135\\P(X\leq 1)=0.99573[/tex]
Hence, the probability that no more than one of the flights will be canceled is 0.99573
