Danny T. answered • 03/01/17
Tutor
5
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A Computer Engineer for Math tutoring (Algebra to Calculus)
There are two different way to solve this, one way should be easier than the others:
Probability of 1 or more of them is approved:
Longer way: Find the probability of 1 out of 9 drugs get approved, add the probability of 2 out of 9 drugs get approved, add the probability of 3 out of the 9 drugs are approved, .... to add the probability of 9 out of 9 drugs get approved.
Probability of 1: 9C1(.09)1(.91)8 = 9(.09)1(.91)8 = .3809045474
Probability of 2: 9C2(.09)2(.91)7 = 36(.09)2(.91)7 = 0.1506875132
Probability of 3: 9C3(.09)3(.91)6 = 84(.09)3(.91)6 = .0347740415
Probability of 4: 9C4(.09)4(.91)5 = 126(.09)4(.91)5 = .0051587864
Probability of 5: 9C5(.09)5(.91)4 = 126(.09)5(.91)4 = .0005102096
Probability of 6: 9C6(.09)6(.91)3 = 84(.09)6(.91)3 = .0000336402
Probability of 7: 9C7(.09)7(.91)2 = 36(.09)7(.91)2 = .0000014259
Probability of 8: 9C8(.09)8(.91)1 = 9(.09)8(.91)1 = .0000000353
Probability of 9: 9C9(.09)9(.91)0 = 1(.09)9(.91)0 = .0000000004
Probability >= 1: .3809045474 + 0.1506875132 + .0347740415 + .0051587864 + .0005102096 + .0000336402 + .0000014259 + .0000000353 + .0000000004 = 0.5720701999 = 57.2%
Shorter way: 1 - Probability of none get approved
Probability of 0: 9C0(.09)0(.91)9 = 1(.09)0(.91)9 = 0.4279298001
Probability >= 1: 1 - 0.4279298001 = .5720701999 = 57.2%
