Please explain step by stetp.. thank you in advance... The probability that a ne
ID: 2954410 • Letter: P
Question
Please explain step by stetp.. thank you in advance... The probability that a new airport will get an award for itsdesign is 0.16, the probability that will get an award for theefficient use of materials is 0.24, and the probability that itwill get both awards is 0.11 (a) what is the probability that it will get at lease one ofthe two awards? (b) what is the probability that it will get only one of twoawards? Please explain step by stetp.. thank you in advance... The probability that a new airport will get an award for itsdesign is 0.16, the probability that will get an award for theefficient use of materials is 0.24, and the probability that itwill get both awards is 0.11 (a) what is the probability that it will get at lease one ofthe two awards? (b) what is the probability that it will get only one of twoawards?Explanation / Answer
This question is best understood with set theory: Assume set A be the event that airport gets award for itsdesign then P(A) or probability of event A is given as 0.16 Similarly Assume set B be the event that airport gets award for efficient useof material then P(B) or probability of event B is given as 0.24 The event that it gets both the awards is A intersection B and Probability of getting at least one award is A union B since A union B = A + B - A intersection B the same holds for probabilities or P(A union B) = P(A) + P(B) - P(A intersection B) thus for part a) = 0.16 + .24 - .11 = 0.29 b) to get only one award it can be either event A happening withevent B not happening or Event B happening and event A nothappening Since P(A) + P ( A not happening) = 1 P ( A not happening) = 1 - P(A) = 1-.16 = .84 similarly P ( B not happening) = 1 - P(B) = 1-.24 = 0.76 substituting the same and noting that the required probabilityis P ( A not happening)* P(B) + P(A)*P ( B not happening) Probability of events happening together are added where asprobability of events exclusive to each other are added thus answer = 0.84*0.24+0.16*0.76 = 0.3232