Question 1Suppose that after 10 years of service, 42% of computers have problems with motherboards (MB), 38% have problems with hard drives(HD), and 21% have problems with both MB and HD.(a) What is the probability that a 10-year old computer have problem with MB or HD. (Write your answer in Blank #1)(B) What is the probability that a 10-year old computer still has fully function MB and HD? (Write your answer in Blank #2)(C) What is the probability that a 10-year old computer have problems with MB but no problems with HD? (Write your answer in Blank#3)Question 2A fair coin is tossed three times. Let X be number of heads.(1) Write out the sample space.(2) Find P(X=2)(3) Find E(X).AnveQuestion 3

Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a time so we are answering the first one as you have not mentioned which one you are looking for. Please re-submit the question separately for the remaining question. Q.1) Let M denotes the event that a 10-year-old computer has a problem with MB and H denotes the event that a 10-year-old computer has a problem with HD. After 10 years of service, 42% of computers have problems with motherboards (MB), 38% have problems with hard drives (HD), and 21% have problems with both MB and HD. So, P(M)=0.42, P(H)=0.38 and P(M∩H)=0.21.a) The required probability is PM∪H=P(M)+P(H)-P(M∩H)=0.42+0.38-0.21=0.59 So, the probability that a 10-year-old computer has a problem with MB or HD is 0.59.b) A 10-year-old computer still has fully functional MB and HD means both MB and HD of the 10-year-old computer do not have problems. So, the required probability is PMc∩Hc=PM∪Hc=1-PM∪H=1-0.59=0.41 The probability that a 10-year-old computer still has fully function MB and HD is 0.41. c) The required probability is PM∩Hc=P(M)-PM∩H=0.42-0.21=0.21 We know that for any two events E and F, PE∩Fc=P(E)-PE∩F. The probability that a 10-year old-computer has problems with MB but no problems with HD is 0.21.