Question

2. Suppose that for an experimental device setup we have to choose settings for three parameters. There are 4, 3 and 5 settings for parameters 1, 2 and 3 respectively. The order in which the settings will be chosen is not does not matter. How may configurations does the device allow? A random sample of 8 configurations is selected. What is the probability that among the configurations in the sample all three settings for parameter 2 are used.

Answer 1

Answer:

Utilizing Theorem of tallying we realize that, since there are 4 settings for boundary 1,3 settings for boundary 2 and 5 settings for boundary 3, along these lines all out setups that the gadget permits is = (4 * 3 * 5)

= 60 .

Presently for the other piece of the inquiry we can consider the settings for boundary 1 and 3 are one substance and that for boundary 2 is another element.

In this manner, out of 8 examples of designs ,3 settings that for boundary 2 can be chosen in 8C3 manners the likelihood of a similar occasion happening is

= (3/12)^3 * (9/12)^5

= 0.0037

3/12 is likelihood of occasion of settings for boundary 2 being utilized and 9/12 is likelihood of occasion of settings for boundary 1 and 3 being used.

In this manner, the likelihood that among the arrangements in the example every one of the three settings for boundary 2 are used

= 8C3 * (3/12)^3 * (9/12)^5

= 0.2076