Assignment Details - Answer ALL the Questions 

Part A 

A.1 A box contains 5 red, 4 blue and 3 white balls. Four balls are selected at random from the 

a) What is the probability that exactly 3 balls are red? 

b) What is the probability that all the four balls are in 2 different colour? 

c) What is the probability that the first and the last ball are white? 

d) Suppose that we win $2 for each red ball selected, lose $1 for each blue ball selected and lose $2 for each white ball selected. What is the probability that we will win the money? 

A.2 For an electronics plant, the maximum number of fire incidents occurring every quarter was reported to be 5. The fire incidents per quarter with the latest 10 years were summarized as below. Assume that the fire incidents occur independently every quarter. 

a) List the probability distribution of the no. of fire incidents per quarter for the plant. 

b) What is the probability that at least 2 fire incidents will occur in next quarter given that no fire incidents occur in this quarter? 

c) What is the standard deviation of no. of fire incidents per quarter? 

d) To control the fire incident rate, a penalty of $50,000 per fire incident will be incurred when 3 or less fire incident occur in a quarter and a severe penalty of $300,000 in total will be incurred when 4 accidents occur and the highest penalty of $800,000 in total will be incurred when 5 accidents occur in a quarter. How much will be expected to pay for the penalty annually? 

A.3 The company buys 70% of its light bulbs from supplier A, 20% from supplier B and 10% from supplier C. Past experience has shown that the light bulbs from supplier A are as likely to be defective as those from supplier B but those defective bulbs from supplier C are 3 times likely as those from supplier B. If a light bulb is chosen at random from the stock and found to be defective

a) What is the probability that the defective light bulb was made by supplier C?

b) What is the probability that the defective light bulb was NOT made by supplier A? 

A.4 Assume the average number of false alarms occurring at a certain commercial building is 2 per week. It is assumed that the Poisson process applies to the random variable “number of false alarms”. 

a) What is the probability that there will be no false alarms in any particular week?

b) What is the probability of finding not more than 2 false alarms in a week?

c) What is the probability that there will be exactly 1 false alarm on Saturday of a week?