Past experience shows that about 75% of all full-scale tested wing designs are acceptable, which means that they can withstand the stress of normal ‡flight. Wind tunnel testing of small-scale models reduces development cost. 90% of all acceptable wing designs also pass the (small-scale) wind tunnel test. Unfavorable wind tunnel data were obtained on 95% of all wings, that fail in full-scale testing. Find the probability that a randomly selected wing design
(a) passes both, wind tunnel and full-scale testing.
(b) passes the wind tunnel but fails the full-scale testing.
(c) passes the wind tunnel test.
(d) Calculate the probability that a wing design which passed the wind tunnel test will also pass full scale
testing.
My work:
a.) My thoughts were that the probability of this would be = 90%(the ones that passed wind tunnel & full scale) of 75%(the ones that passed full-scale)= (90/100)(75/100)=27/40=0.675
b.) 5%(the ones that passed wind tunnel but failed full scale) of 25%(the ones that failed full scale)=(5/100)(25/100)=1/80=0.0125
c.)P(passes wind tunnel)=(0.675)+(0.0125)=0.6875
d.) (Using Baye's Theorem), I came up with P(passed full scale given passed wind scale) = [P(passed wind tunnel given passed full scale)*P(passed full scale)]/[P(passed wind tunnel)]=[(90%)(75%)]/[(75%)(90%)+(25%)(5%)]=54/55=0.982
Did I do this right?
Thank you for any feedback given!
(a) passes both, wind tunnel and full-scale testing.
(b) passes the wind tunnel but fails the full-scale testing.
(c) passes the wind tunnel test.
(d) Calculate the probability that a wing design which passed the wind tunnel test will also pass full scale
testing.
My work:
a.) My thoughts were that the probability of this would be = 90%(the ones that passed wind tunnel & full scale) of 75%(the ones that passed full-scale)= (90/100)(75/100)=27/40=0.675
b.) 5%(the ones that passed wind tunnel but failed full scale) of 25%(the ones that failed full scale)=(5/100)(25/100)=1/80=0.0125
c.)P(passes wind tunnel)=(0.675)+(0.0125)=0.6875
d.) (Using Baye's Theorem), I came up with P(passed full scale given passed wind scale) = [P(passed wind tunnel given passed full scale)*P(passed full scale)]/[P(passed wind tunnel)]=[(90%)(75%)]/[(75%)(90%)+(25%)(5%)]=54/55=0.982
Did I do this right?
Thank you for any feedback given!
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