Suppose that an assembly consists of 16 solder joints and th

Suppose that an assembly consists of 16 solder joints and that unknown to the researcher 5 of these solder joints are cracked If the researcher randomly chooses a sample of 4 of the solder joints for inspection then the state space of the number of cracked joints in the sample is {0,1, 2, 3, 4} What is the probability that there will be exactly two cracked solder joints in the researchers sample? 3020 1820 0357 0055

Solution

Total solder joints = 16

Of these cracked = 5

n = Sample size = 4

X - no of cracks in the sample 4 is binomial with p = 5/16 = 0.3125 and n =4

Prob for exactly 2 cracks in 4 = P(x=4)

= 4C2 (0.3125)²(1-0.3125)^4-2

= 0.2769

Hence none of the options is right.