Question

. In a given year, approximately 1% of all flights sched- uled to depart from US airports are canceled (source: Department of Transportation Statistics, Intermodal Data Base). You select 10 flights at random. Use the binomial probability function to compute the proba- bility that a. none of the flights will be canceled. b. exactly one of the flights will be canceled. c. no more than one of the flights will be cancele

Answer 1

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: $P(X) = ^nC_x p^x q^{n-x}$

Part  a. none of the flights will be canceled.

$P(X=0)=^{10}C_0 (0.01)^0 (0.99)^{10}=0.90438$

Hence, the required probability of none of flights will be canceled is 0.90438

Part b. exactly one of the flights will be canceled.

$P(X=1) = ^{10}C_1 (0.01)^1 (0.99)^{9}=0.09135$

Hence, the probability that exactly one will be cancelled is 0.09135

Part c. no more than one of the flights will be canceled.

$P(X\leq 1) = P(X=0)+P(X=1)\\P(X\leq 1)=0.90438+0.09135\\P(X\leq 1)=0.99573$

Hence, the probability that no more than one of the flights will be canceled is 0.99573