A computer can be classified as either cutting dash edge or ancient. Suppose that 86% of computers are classified as ancient. (a) Two computers are chosen at random. What is the probability that both computers are ancient? (b) Seven computers are chosen at random. What is the probability that all seven computers are ancient? (c) What is the probability that at least one of seven randomly selected computers is cutting dash edge? Would it be unusual that at least one of seven randomly selected computers is cutting dash edge?
Accepted Solution
A:
Answer:(a) The probability that both computers are ancient is 0.7396(b) The probability that all seven computers are ancient is 0.3479(c) The probability that at least one of seven randomly selected computers is cutting dash edge is 0.6520. Because the probability is about 65% is it not unusual that at least one of seven randomly selected computers is cutting dash edge, it's more likely than not.Step-by-step explanation:We know that 86% of computers are classified as ancient. This means, if one computer is chosen at random, there is an 86% chance that it will be classified as ancient. [tex]P(ancient)=0.86[/tex] (a) To find the probability that two computers are chosen at random and both are ancient you must,The probability that the first computer is ancient is [tex]P(ancient)=0.86[/tex] and the probability that the second computer is ancient is [tex]P(ancient)=0.86[/tex] These events are independent; the selection of one computer does not affect the selection of another computer.When calculating the probability that multiple independent events will all occur, the probabilities are multiplied, this is known as the rule of product.Let A be the event "the first computer is ancient" and B the event "the second computer is ancient".[tex]P(A\:and \:B)=P(A)\cdot P(B)=0.86\cdot 0.86=0.86^2= 0.7396[/tex](b) To find the probability that seven computers are chosen at random and all are ancient you must,Following the same logic in part (a) we haveLet A be the event "the first computer is ancient", B the event "the second computer is ancient", C the event "the third computer is ancient", D the event "the fourth computer is ancient", E the event "the fifth computer is ancient",F the event "the sixth computer is ancient", andG the event "the seventh computer is ancient"[tex]P(A\:and \:B\:and \:C\:and \:D\:and \:E\:and \:F\:and \:G)=\\P(A)\cdot P(B)\cdot P(C)\cdot P(D)\cdot P(E)\cdot P(F)\cdot P(G) =(0.86)^7=0.3479[/tex](c) To find the probability that at least one of seven randomly selected computers is cutting dash edge you mustUse the concept of complement. The complement of an event is the subset of outcomes in the sample space that are not in the event.Let C the event "the computer is cutting dash edge".Let A the event "the seven computers are ancient".[tex]P(C)=1-P(A)=1-0.3479=0.6520[/tex]Because the probability is about 65% is it not unusual that at least one of seven randomly selected computers is cutting dash edge, it's more likely than not.