AP EAMCET202315 May 2023Evening ShiftMathematicsProbabilityActual
Three screws are drawn at random from a lot of 50 screws containing 5 defective ones. Then the probability of the event that all 3 screws drawn are non-defective, assuming that the drawing is (a) with replacement (b) without replacement respectively is
Options
- A( 9 10 )^3, 1419 1960
- B( 9 10 )^2, 1418 1961
- C( 9 10 )^2, 1419 1960
- D( 9 10 )^3, 1418 1961
Correct answer
A. ( 9 10 )^3, 1419 1960
Step-by-step solution
Given total screws =50 defective screws =5 and non-defective screws =45 Let A be the event of getting drawing of 3 screws are not defective. (a) with replacement, P(A)= ( ⁴⁵ C₁ ⁵⁰ C₁ )^3= ( 9 10 )^3 (b) without replacement aligned & P(A)= ⁴⁵ C₁ ⁵⁰ C₁ ⁴⁴ C₁ ⁴⁹ C₁ ⁴³ C₁ ⁴⁸ C₁ & = 45 50 44 49 43 48 = 1419 1960 aligned