I need help with this probability question. I have tried and Ijust can\'t seem t
ID: 2919280 • Letter: I
Question
I need help with this probability question. I have tried and Ijust can't seem to understand it! A spacecraft has three engines. The craft fails when all threeof its engines fail. The failure of the engines of the spacecraftare indepent events. For any engine, the probability of failure inthe first year the craft operates is 0.4, the probability offailure in the second year of operation is 0.2, and the probabilitythat it fails in the third year is 0.1. A new spacecraft is builtand sent into orbit today. (a) Find the probability the craft is operating after 2years (b) Find the probability the craft is operating after 3years (c) Find the probability the craft is operating after 2 years,but fails by the end of its 3rd year Thanks! I need help with this probability question. I have tried and Ijust can't seem to understand it! A spacecraft has three engines. The craft fails when all threeof its engines fail. The failure of the engines of the spacecraftare indepent events. For any engine, the probability of failure inthe first year the craft operates is 0.4, the probability offailure in the second year of operation is 0.2, and the probabilitythat it fails in the third year is 0.1. A new spacecraft is builtand sent into orbit today. (a) Find the probability the craft is operating after 2years (b) Find the probability the craft is operating after 3years (c) Find the probability the craft is operating after 2 years,but fails by the end of its 3rd year Thanks!Explanation / Answer
a) P(operating after two years)= 1-P(all three engines fail in thefirst two years) =1-(P(an engine fail in either the first or secondyear))3 =(1-0.63 =0.784 b) P(operating after 3 years)= 1-P(all three engines fail in thefirst 3 years) =1-(P(an engine fail in either the first or second year or thirdyear))3 =(1-(0.4+0.2+0.1)3) =0.657 c) answer from part a - answer from part b =0.784-0.657 =0.127