Marine researchers in the UK recently conducted a study of oil spills from oil t

Question

Marine researchers in the UK recently conducted a study of oil spills from oil tankers that run aground. Using historical data, the study reported that if a tanker goes aground, there is a 30% change that it will spill oil. Suppose 15 tankers go aground in the next year. Assume that the spills are independent of one another. Include the definition of any variables that you use.

a) [3marks]Whatistheprobabilitythatexactlyfourofthetankerswillspilloil?
b) [5marks]Whatistheprobabilitythatnomorethanoneofthetankerswillspilloil?

c) [2 marks] What is the expected number of tankers that will not spill?

Explanation / Answer

p = 0.3

n = 15

This is a binomial distribution

P(X = x) = 15Cx * 0.3x * (1 - 0.3)15-x

a) P(X = 4) = 15C4 * 0.34 * 0.711

                  = 0.2186

b) P(X > 1) = 1 - P(X < 1)

                  = 1 - [P(X = 0) + P(X = 1)]

                  = 1 - [15C0 * 0.30 * 0.715 + 15C1 * 0.31 * 0.714]

                  = 1 - 0.0353

                  = 0.9647

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