The probability of the safe arrival of one ship out of 5 is 1/5. What is the probability of the safe arrival of at least 3 ships?

Question

The probability of the safe arrival of one ship out of 5 is \(\frac{1}{5}.\) What is the probability of the safe arrival of at least 3 ships?

A. \(\frac{1}{31}\)

B. \(\frac{3}{52}\)

C. \(\frac{181}{3125}\)

D. \(\frac{184}{3125}\)

Answer 1

The probability of safe arrival of the ship is 1/5

Using Bernoulli’s Trial we have,

P(Success=x) \(=n_{C_x}.p^x.q^{(n-x)}\)

x = 0, 1, 2, ………n and q = (1 - p), n = 5

p = 1/5 , q = 4/5

Probability of safe arrival of at least 3 ships is = P(3)+P(4)+P(5)