From the 5 defective parts, select 4, and the number of ways to complete this step is 5!/(4!1!) = 5From the 45 non-defective parts, select 6, and the number of ways to complete this step is 45!/(6!39!) = 8,145,060Therefore, the number of samples that contain exactly 4 defective parts is 5(8,145,060) = 40,725,300Similarly, from the 5 defective parts, the number of ways to select 5 is 5!(5!1!) = 1From the 45 non-defective parts, select 5, and the number of ways to complete this step is 45!/(5!40!) = 1,221,759Therefore, the number of samples that contain exactly 5 defective parts is 1(1,221,759) = 1,221,759Finally, the number of samples that contain at least 4 defective parts is 40,725,300 + 1,221,759 = 41,947,059Total possible: 1016, but only 108are valid. Therefore, P(valid) = 108/1016= 1/108Apply addition rule: (a) P(unsatisfactory) = (5 + 10 – 2)/130 = 13/130(b) P(both criteria satisfactory) = 117/130 = 0.90, No(a) P = (8-1)/(350-1)=0.020(b) P = (8/350) [(8-1)/(350-1)]=0.000458(c) P = (342/350) [(342-1)/(350-1)]=0.9547(a) (0.88)(0.27) = 0.2376(b) (0.12)(0.13+0.52) = 0.0.078P(X = 10 million) = 0.3, P(X = 5 million) = 0.6, P(X = 1 million) = 0.1The sum of the probabilities is 1 and all probabilities are greater than or equal to zero: f(-10) = 0.25, f(30) = 0.5, f(50) = 0.25a) P(X50) = 1b) P(X40) = 0.75c) P(40 X 60) = P(X=50)=0.25d) P(X<0) = 0.25e) P(0X<10) = 0f) P(10<X<10) = 0Let X denote the number of trials to obtain the first successful alignment. Then X is a geometric random variable with p = 0.8 a) 0064.08.02.08.0)8.01()4(33XP b) )4()3()2()1()4( XPXPXPXPXP 8.0)8.01(8.0)8.01(8.0)8.01(8.0)8.01(3210 9984.08.02.0)8.0(2.0)8.0(2.08.032 c) )]3()2()1([1)3(1)4( XPXPXPXPXP ]8.0)8.01(8.0)8.01(8.0)8.01[(1210
View Full Document
Unlocking...