Question

the probabilities are 0.4, 0.2, 0.3, and 0.1, respectively, that a delegate to a certain convention arrived by air, bus, automoile, or train. consider 9 randomly selected delegates at this convention. suppose we are only interested in the delegates arriving by air. what is the probability that the number of delegates arrived by air is less than 7

Answer 1

The probability that the delegates arrives by aur is less then 7 is 0.98.

Given that the probability that a delegate to a certain convention arrived by air = 0.4

the probability that a delegate to a certain convention arrived by bus = 0.2

the probability that a delegate to a certain convention arrived by automobile = 0.3

the probability that a delegate to a certain convention arrived by train = 0.1

We have to calculate the probability that the number of delegates arrived by air is less than 7


When 7 delegates arrives by air and 2 by bus
=(0.4^7)*(0.2^2)*(FACT(9)/(FACT(7)*FACT(2))

When 7 delegates arrives by air and 2 by automobile = (0.4^7)*(0.3^2)*(FACT(9)/(FACT(7)*FACT(2))

When 7 delegates arrives by air and 2 by train = (0.4^7)*(0.1^2)*(FACT(9)/(FACT(7)*FACT(2))

When 8 delegates arrives by air and 1 by bus = (0.4^8)*(0.2^1)*(FACT(9)/(FACT(8)*FACT(1))

When 8 delegates arrives by air and 1 by automobile = (0.4^8)*(0.3^1)*(FACT(9)/(FACT(8)*FACT(1))

When 8 delegates arrives by air and 1 by train = (0.4^8)*(0.1^1)*(FACT(9)/(FACT(8)*FACT(1))

When all 9 delegates arrives by air = (0.4^9)*(FACT(9)/(FACT(9)

On calculation We get 1- 0.02 = 0.98
the probability that delagates arrives by air is less then 7 is 0.98

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