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Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability  Exercise 30.4 Question 16 Maths Textbook Solution.

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Answer: 0.8645

Given: An article manufactured by a company consists of two parts X and Y. In the process of manufacture of the part X, 9 out of 100 parts may be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of part Y.

Hint: Probability=\frac{No\: of\: outcomes}{Total\: outcomes}

Solution:

Let, A= Particle X is defective

      B= Particle Y is defective

            P\left ( A \right )=\frac{9}{100}

            P\left ( B \right )=\frac{5}{100}

Required Probability =P\left ( \bar{A}\cap \bar{B} \right )

                               \begin{aligned} &=\mathrm{P}(\overline{\mathrm{A}}) \times \mathrm{P}(\overline{\mathrm{B}}) \\ &=[1-\mathrm{P}(\mathrm{A})][1-\mathrm{P}(\mathrm{B})] \\ &=\left[1-\frac{9}{100}\right]\left[1-\frac{5}{100}\right] \\ &=\frac{91}{100} \times \frac{95}{100} \\ &=0.8645 \end{aligned}

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