Question

Consider the following hypergeometric experiment. Electric fuses produced by Ontario Electric are packaged in boxes of 12 units each. An inspector randomly selects three of the 12 fuses in a box for testing. If the box contains exactly five defective fuses, the probability that the inspector will find exactly one of the three fuses defective is __________. The probability of finding at least 1 defective fuse is __________. NOTE: Write your answers in number format, with 2 decimal places of precision level. Add a leading minus sign symbol, a leading zero and trailing zeros, when needed. Use a period for the decimal separator and a comma to separate groups of thousands.

Answer 1

Let X = the number of defective fuse selected.
N: The number of items in the population = 12
k: The number of items in the population that are classified as successes i.e. defective in this example = 5
n: The number of items in the sample = 3
x: The number of items in the sample that are classified as successes.
kCx: The number of combinations of k things, taken x at a time.
h(x; N, n, k) = [ kCx ] [ N-kCn-x ] / [ NCn ]

Question1:
P[X=1] = h(1;12,3,5)
=(5C1)*(7C2)/(12C3)
=5*21/220
=0.48

Question2:
P[X>=1] = P[X=1]+P[X=2]+P[X=3] = 1 - P[X=0]
= 1 - h(0;12,3,5)
= 1 -(5C0)*(7C3)/(12C3)
= 1 - 1*35/220
= 0.84

Consider the following hypergeometric experiment. Electric fuses produced by Ontario Electric are packaged in boxes of 12 units each. An inspector randomly selects three of the 12 fuses in a box for testing. If the box contains exactly five defective fuses, the probability that the inspector will find exactly one of the three fuses defective is 0.48. The probability of finding at least 1 defective fuse is 0.84. NOTE: Write your answers in number format, with 2 decimal places of precision level. Add a leading minus sign symbol, a leading zero and trailing zeros, when needed. Use a period for the decimal separator and a comma to separate groups of thousands.