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  • From a lot of 20 bulbs which include 5 defectives, a sample of 3 bulbs is drawn at random, one by one with replacement. Find the probability distribution of the number of defective bulbs. Also, find the mean of the distribution.  

From a lot of 20 bulbs which include 5 defectives, a sample of 3 bulbs is drawn at random, one by one with replacement. Find the probability distribution of the number of defective bulbs. Also, find the mean of the distribution.

 

 

 

 
 
 
 
 

Answers (1)

Let x: no.of defective bulbs. so x = 0,1,2,3
Total bulbs : = 20 and defective bulbs = 5
Let E : the defective bulb is drawn, so p\left ( E \right )= \frac{5}{20}= \frac{1}{4}= p,p\left ( \vec{E} \right )= \frac{3}{4}= q
As a sample of 3 bulb is drawn so, n = 3, hence p\left ( x= r \right )=\, ^{3}C_{r}\left ( \frac{1}{4} \right )^{r}\left ( \frac{3}{4} \right )^{3-r}= r= 0,1,2,3
\therefore the following table represents the required probability distribution:

x 0 1 2 3
p\left ( x \right ) \frac{27}{64} \frac{27}{64} \frac{9}{64} \frac{1}{64}

 Also mean \sum x \times p\left ( x \right )= 0+\frac{27}{64}+\frac{18}{64}+\frac{3}{64}= \frac{48}{64}= \frac{3}{4}

Posted by

Ravindra Pindel

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