KCET2017MathematicsArea Under Curves
A box has ( 100 ) pens of which ( 10 ) are defective. The probability that out of a sample of ( 5 ) pens drawn one by one with replacement and at most one is defective is
Options
- A( 9 10 )
- B( 1 2 ( 9 10 )⁴ )
- C( ( 9 10 )⁵+ 1 2 ( 9 10 )⁴ )
- D( 1 2 ( 9 10 )⁵ )
Correct answer
C. ( ( 9 10 )⁵+ 1 2 ( 9 10 )⁴ )
Step-by-step solution
Given that, probability of defective pens is [ P= 10 100 = 1 10 ] So, probability of non-defective pens is [ array l Q=1-P= 9 10 Since, n=5, x 1 . So, P(x 1)=P(x=0)+P(x=1) = 5 0 ( 1 10 )⁰ ( 9 10 )⁵+ 5 1 ( 1 10 )¹ ( 9 10 )⁴ = ( 9 10 )⁵+ 1 2 ( 9 10 )⁴ array ]