Question

1. Present the following by using a Venn diagram. (10 marks) (ANC) UB (A) B (AUC) B(AUCnB (AUCB (ANC)UB (An)UB (AUC) NB(ANBUC (AB) UC (7 marks) A private pilot wishes to insure his airplane for RM200k. The insurance company estimates that a total loss many occur with probability 0.2%, a 50% loss with probability 1%, and a 25% loss with probability 10%. Ignoring all other partial losses, what premium should the insurance company charge each year to realize an average profit of RM500? (8 marks) The safety director for a manufacturing company reports that industrial accidents requiring medical treatment occur randomly and independently of one another at the rate 3 accidents per month. Find the probability that at most 3 accidents occur in a given month. Suppose the manufacturing company establishes a safety goal that pledges to reduce accidents requiring medical treatment to no more than one accident per month. For a given two months, find the probability that the safety goal is met (5 marks) A company mass produces electronic calculators. From past experience it knows that 10% of the calculators will be faulty and 90% will be in working ordered if the production process is working satisfactorily. An inspector randomly selects 5 calculators from the production line every hour and carries out a rigorous check. What is the probability that a random sample of $ will contain more defective calculator compare to in working ordered calculator?

Answer 1

(2) from the given data, The insurance company estimates that a total loss - RM Look will occur with probability 0.2% (0.002). we need to find the expected payment by insurance company is Expected loss = Sam (probability of loge loss value] 5900,000[1*0.662 +0.5 *0.01 +0.25 *oi] = 200.000 (0.032] = buso Ignoring all other partial loses the insurance company charge each year a profit of RM 500 of premium is premium amount = RM 6uro + RM Sto - RM 6900 Ang (3) let x be a poisson randon variable which denotes the number of accidents: x= 3 per month The probability that at most a accidents occur in a given = P(x=3) = P(x=0)+ P(x-1) +P(x=1) +P(X=3) - €3(1+3+ . for a given two months, average noot accidents = 3(2) = 6 To meet the gatety goal there ghould be no more than two accidents the probability of which is - 0.6472 -6 (1767 e 20.0620Any.

(4) probability of an electronic calculators to be faulty = 0.10 probability of an electronic calculator to be in working Condition = 0.90 when selected 5 calculators at Tandon, Cases that there will be more detective calculators compared to wooking ordered calculator will be Cage 1 3 detective and a working Cage 2 u detective and I working Cage 3: 5 defective and o working Before looking at the probabilities at uz tiset fanuliarulize augelves with the concept at binomial probability distribu- tien. In such cars we have a posebilities such that the Sun of probabilities of both the cases is let the probability of detective be p.. so out of n cases the detective probability that it will be for or no.ct cases will be ncr x prxli-pinet Now, let's look at their probabilities for this case! Cage 1 - probability = 5G X 0.10 0.90% = 0.0081 Cage 2: Papable+ : 5c, холочке-16 . o.eees Case 3: se probability = 5Cg *0:105x 0.18 = 0.0000! . .. Required probability = 0.0081 +0.oochs +0.0oool 0.00556 Ang Not: As por HomeworkLib rules, I have to do the angwer with in 2 hours and you posted the u questions. There is no time to do the ongewer from 1st question se, I don't have the time to draw the venn diagrams. please repost that question. If you have any doubt, please comment. If it is ugetul to you, please LIKE (THUMBS Up) it. THANK you.