A new factory machine which manufactures computer chips is malfunctioning and has a 20% defect rate. If 5 chips are randomly selected from the machine, find the following probibilities: non are defective; less than 2 are defective.
The probability that is would be correct is $\displaystyle .8$, just let us use fractions which is $\displaystyle \frac{4}{5}$. Now each 5 should be correct thus,Originally Posted by batman123
$\displaystyle \left(\frac{4}{5}\right)^5\approx .33$.
For the second part you need to use the formula:
$\displaystyle _nC_mp^m(1-p)^{n-m}$ to determine the probability of something exactly happening out of a certain amount of times.
Over here you need it to be zero times exactly OR one time exactly of getting a defect. Zero times is the same as all 5 where non-defective which is the same as in the first problem is 33%. To determine of getting exactly one defect use $\displaystyle _5C_1\left(\frac{4}{5}\right)^4\left(\frac{1}{5} \right)^{5-4}\approx .4$. Thus, the overall probability is the sum which is approximately 73%.
This is my 5th post!!