Find the Probability

Mathematics
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a box contains 13 transistors, 5 of which are defective. If 5 are selected at random, find the probability that
Sep 30th, 2015

Thank you for the opportunity to help you with your question!

To calculate the probability that a number of transistors are defective, we will make an assumption/postulation that the transistors are randomly and uniformly distributed or placed in the box.

The probability that X number of transistors picked is calculated as follows:-

X/5 * 5/13

5/13 is the probability of picking a defective transistor.

1/5 is the probability of picking one defective transistor from the five defective transistors.

Hence X/5 is the probability of picking X defective transistors from the five transistors.


For example the probability that 3 of the transistors picked are defective is given by,

3/5 * 5/13 = 3/13 or 0.2307 or 23.07%

NB

* stands for multiplication

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 30th, 2015
a box contains 13 transistors, 5 of which are defective. If 5 are selected at random, find the probability that a. all are defective b. none are defective
Sep 30th, 2015

Continuing from the explanation above;

a. if all are defective, the following are the events,

(D and D and D and D and D)

D stands for the probability of picking a defectivetransistor while ND stands for non defective

the probability of D is 5/13 for the first pick.

In probability "and" means multiplication since these are joint events.

Therefore the probability that all transistors picked are defective is given by 5/13*4/12*3/11*2/10*1/9 =120/154440 =0.0777%

b. The probability that none of the transistors picked are defective is the probability that all transistors picked are non defective.

Events

(ND and ND and ND and ND and ND)

=(8/13*7/12*6/11*5/10*4/9) = 6720/154440 = 4.3512%

Note: I have changed the formula and method of calculation since your follow up question implies a method where the transistors are picked without replacement.

Sep 30th, 2015

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