question_answer

  In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective? Write two advantages of using CFL (compact fluroscent lamp) bulbs over incandescent bulbs.           

Answer:

Given in a box containing n = 100 bulbs, 10 are defective. Let the number of non-defective bulbs. In this sample be X. P (getting a defective bulb) \[\Rightarrow \]               \[P=\frac{10}{100}=\frac{1}{10}\] \[q=1-p=1-\frac{1}{10}=\frac{9}{10}\] Since X has a binomial distribution, the probability of X success in n-Bernoulli trials. \[p\,(X=x)={}^{n}{{C}_{x}}\cdot {{p}^{x}}\cdot {{q}^{n\,-\,x}},\]where \[x=0,\,\,1,\,\,2,\,\,....n\]and \[(q=1-p)\] p (none of bulbs are defective) \[=p\,(X=0)={}^{5}{{C}_{0}}\cdot {{\left( \frac{1}{10} \right)}^{0}}{{\left( \frac{9}{10} \right)}^{5\,-\,0}}\] \[={}^{5}{{C}_{0}}\cdot {{\left( \frac{1}{10} \right)}^{0}}{{\left( \frac{9}{10} \right)}^{5}}={{\left( \frac{9}{10} \right)}^{5}}\] Advantages (i) Uses energy more efficiently (saves energy) (ii) Lower price (iii) Releases lesser amount of heat.