Question

Show brief working, or sketch a figure, and write down the MATLAB function calls you use to calculate probabilities (e.g. binocdf(2,15,1)) Q1 Let A be the event that oil is struck at location A on the sea bed, and B be the event that oil is struck at location B on the sea bed. The probabilities of A and B are 0.5 and 0.3 respectively. The probability of both A and B is 0.2. (i) What is the probability of A or B? (ii) What is the probability of A given B? (111) If it costs 10 million to drill and the revenue if oil is found is 20 million per well what is the expected return? [3 marks]

Answer 1

Given

$P(A) = 0.5, P(B) = 0.3, P(A\cap B) = 0.2$

i) The probability of A or B

$= P(A\cup B)$

$= P(A) + P(B) - P(A\cap B)$

$= 0.5 + 0.3 - 0.2$

$= 0.6$

ii) The probability of A given B

$= P(A|B)$

$= \frac{P(A\cap B)}{P(B)}$

$= \frac{0.2}{0.3}$

$= 0.666667$

iii) The expected return is

$= 20*P(A) + 20*P(B) - 10$

$=(20*0.5)+ (20*0.3) - 10$

$= 6$