CBSE Class 12-science Answered

Probability of defective p_d = 0.1 ; Probability of non-defective p_nd = 0.9

Probabity of getting exactly two defective pen if 12 pens are chosen is obtained from binomial probability distribition.

Probabity p(2) of getting exactly two defective pen is

p(r=2) = ¹²C₂ ( 0.1 )² (0.9)¹⁰ = 0.230

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Probabity p(0) of not getting any defective pen is

p(r=0) = ¹²C₀ ( 0.1 )⁰ (0.9)¹² = 0.282

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Probabity p(r=1) of getting exactly one defective pen is

p(r=1) = ¹²C₁ ( 0.1 )¹ (0.9)¹¹ = 0.377

Probability p(r ≥ 2 ) of atleast two defective pen out of 12 pen is

p(r ≥ 2 ) = 1 - p(r=0) - p(r=1) = 1 - 0.282 - 0.377 = 0.341

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