Question

20% of bolts produced by machine are defective .the probability that out of three bolts chossen at random 1 is defective is
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Answer 1

Answer:

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Answer 2

Probability that  out of three bolts chosen at random 1 is defective is  48/125.

Step-by-step explanation:

Given: 20% of bolts are  defective which are produced by machine.

To Find: Probability that out of three bolts chosen at random 1 is defective.

Formula Used:

P(X=k)=nCk $p^{k} q^{n-k}$       -------------  formula no.01

Here, P(X=k) = The probability of  getting k bolts defective  out of  number of n bolts inspected

            n = number of  bolts  chosen

            X= A  random variable which takes value of k

            k = number  of  getting  defective bolts

            p = probability of getting  one defective bolt

            q = probability of not getting defective bolt

Solution:

As given  20% of bolts produced by machines are  defective.

  p = probability of getting  one defective  bolt out of 100

  = 20/100 = 1/5

 q = probability of not getting defective bolt

 q = 1-p

 =1-1/5 =4/5

  n  = 3

  k =  1

 Substituting the value of n,k,p and q in the formula no.01:

  P(X=k)= nCk $p^{k} q^{n-k}$

             =  3C1 $(\frac{1}{5} )^{1}$  $(\frac{4}{5} )^{3-1}$    

             = $\frac{3!}{(3-1)! . 1!}$  $(\frac{1}{5} )$  $(\frac{4}{5} )^{2}$

             = $\frac{3 .2!} {2! . 1!}$ $(\frac{1}{5} )$$(\frac{16}{25} )$

             = $\frac{3}{1}$ $(\frac{1}{5} )$ $(\frac{16}{25} )$

             = $\frac{48}{125}$

Thus,Probability that  out of three bolts chosen at random 1 is defective is  48/125.