Given a set of (10) transistors, (2) of them are defective. Choose a sample of (4) transistors, then 1) find the probability that a sample has: i-One defective transistors. ii-At least one defective transistor. If X is a random variable represent defective transistors in a sample. Then 2) find the probability function f(x) and distribution function F(x). 3) find (by two methods) the probability that a sample has: i-One defective transistors. ii-At least one defective transistor.

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Given a set of (10) transistors, (2) of them are defective. Choose a sample of (4) transistors, then  1) find the probability that a sample has:  i-One defective transistors. ii-At least one defective transistor.  If X is a random variable represent defective transistors in a sample. Then  2) find the probability function f(x) and distribution function F(x).  3) find (by two methods) the probability that a sample has:  i-One defective transistors. ii-At least one defective transistor.

Harr1957 · Accepted Answer

Step 1   Here the probability of a particular event takes place. It is defined as the total outcome of the data divided by the total possible outcome. We have to use the binomial distribution method to calculate values of events either once, twice, thrice, up to the x times in k trials.   1] p= Probability of success   2] q= Probability of failure   3] p+q=1   4] The required probability =rncprqn−r  Step 2   (a)   (i) Generally the number of ways of choosing the 4 transistors from 10 transistors is as follows,  104C=210  Hence the total number of defective transistors out of 10 transistors=2   Number of ways of choosing a defective transistor out of 10 transistors is as follows,  (ii) To find the Probability of choosing at least a defective transistor is equal to choosing one defective transistor plus choosing two defective transistors.  =41cpq3+42cp2q2  =4×120×(1920)3+6×(120)2×(1920)2  =0.1850  Step 3  If x is the defective transistors in a sample of 4  Then there are 210 samples in all, if each sample has 4 transistors with probability function for a sample is equal to 4xcpxq4−x  The distribution function is equal to 120,  If p=mn,m=1 and n=20  =e−m×mxx!  =e−1×1xx!  =1x!e  Step 4   (3) Also,   The probability of choosing the defective transistor out of 10 transistors is as follows,  =21c101c  =210  The sample has 4 transistors probability of choosing one or more defective transistor  =14 or 14+24  =14 or 34  The required probability is as follows,  =15×14  =120

Given a set of (10) transistors, (2) of them are defective. Choose a s

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