Reference no: EM133094136

BIC-0011 Maths for business and social sciences - Bangor University

Question 1: An experiment consists of selecting a ball from a bag and spinning a coin. The bag contains 8 red balls and 12 blue balls. A ball is selected at random from the bag, its colour is noted and then the ball is returned to the bag. When a red ball is selected, a biased coin with probability 1/4 of landing heads is spun. When a blue ball is selected a fair coin is spun.

(a) Complete the tree diagram (in answer book) to show the possible outcomes and associated probabilities.

Shivani selects a ball and spins the appropriate coin.

(b) Find the probability that she obtains a red ball and a head

(c) Find the probability that she obtains a tail

Question 2: An insurance company is looking at pricing up a policy for a new customer. The table below outlines the cost of the items that will be on this policy and the probability that these items are stolen.

(a) What is the expected cost to the insurance company for this policy?

(b) Would £175 be a sensible price to charge for the policy? Explain your answer.

(c) What should the company charge for the policy if it wants to make a 10% profit on average?

Question 3: Xavier, Yuri and Zara all travel to work in the morning via different methods. The probabilities of them arriving late are, independently, 0.1, 0.42 and 0.23 respectively.

(a) Calculate the probability that for a particular day:

i) Only two arrive late.
ii) Only one arrives late.

Another worker, Wei, catches the same bus as Zara but stops off at a shop to buy lunch each morning. The probability that Wei arrives late is 0.92 when Zara arrives late, and is 0.17 when Zara does not arrive late.

b) Calculate the probability that for a particular practice session:

i) Both Zara and Wei arrive late

ii) Either Zara or Wei, but not both, arrives late.

Question 4. Calculate the expected value and state whether the company can expect to make a profit or not.

a. A local club plans to invest £15,000 to host a baseball game. They expect to sell tickets worth £23,000. But if it rains on the day of game, they won't sell any tickets and the club will lose all the money invested. The weather forecast for the day of game is a 42% possibility of rain.

b. A company makes electronic gadgets. One out of every 80 gadgets are faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a £3.23 profit on the sale of any working gadget, but suffers a loss of £74 for every faulty gadget because they must repair the unit.

Question 5: Candidates applying for jobs in a large company take an aptitude test, as a result of which they are either accepted, rejected or retested, with probabilities 0.2, 0.37 and 0.43 respectively. When a candidate is retested for the first time, the three possible outcomes and their probabilities remain the same as for the original test. When a candidate is retested for the second time there are just two possible outcomes, accepted or rejected, with probabilities 0.35 and 0.65 respectively.

(a) Draw a probability tree diagram to illustrate the outcomes.

(b) Find the probability that a randomly selected candidate is accepted.

(c) Find the probability that a randomly selected candidate is retested at least once, given that this candidate is accepted.

Question 6: The lifetimes of bulbs used in a lamp are normally distributed. Your company sells bulbs with a mean lifetime of 1200 hours and a standard deviation of 65 hours.

(a) Find the probability of a bulb, having a lifetime of more than 1300 hours.

(b) Find the probability of a bulb, having a lifetime of less than 1050 hours.

(c) Find the expected number of bulbs having a lifetime of less than 1100 hours, from a box of 500

Attachment:- Maths for business and social sciences.rar