Question

1)Naval intelligence reports that 5 enemy vessels in a fleet of 18 are carrying nuclear weapons. If 9 vessels are randomly targeted and destroyed, what is the probability that more than 1 vessel transporting nuclear weapons was destroyed? Express your answer as a fraction or a decimal number rounded to four decimal places.

2)Cars enter a car wash at a mean rate of 3 cars per half an hour. What is the probability that, in any hour, exactly 2 cars will enter the car wash? Round your answer to four decimal places.

Answer 1

Solution:-

1) The probability that more than 1 vessel transporting nuclear weapons was destroyed is 0.7615.

p = 5/18 = 0.2778

n = 9, x = 1

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 1) = 1 - P(x = 0) + P(x = 1)

P(x > 1) = 1 - (0.05346 + 0.18505)

P(x > 1) = 0.7615

2) The probability that, in any hour, exactly 2 cars will enter the car wash is 0.2240.

Mean = 3

x = 2

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x = 2) = 0.22404