Mathematics: 96% of all air travel departs on time. If you are taking 3 flights in one day, what is the probability that all of them depart on time?

96% of all air travel departs on time. If you are

only1123

05.02.2022

0.884736

Step-by-step explanation:

Given: The proportion of all air travel departs on time: p= 0.96

Total flights : n= 3

Let x be the number of flights on time.

As there are two cases either flight on time or not, so it is a binomial case.

Binomial distribution formula: $P(X=x)=\ ^nC_xp^x(1-p)^{n-x}$

The probability that all of them depart on time = $P(X=3)=\ ^3C_3(0.96)^3(1-0.96)^0=(1)(0.96)^3=0.884736$

The probability that all of them depart on time = 0.884736

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