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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability Exercise 30.4 Question 17 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability  Exercise 30.4 Question 17 Maths Textbook Solution.

Answers (1)

Answer: \frac{3}{5}

Hint: Use, P\left ( A\cup B \right )=P(A)+P\left ( B \right )-P\left ( A\cap B \right )

Given, Possibilities

          P\left ( A \right )=P  (A hits target) =\frac{1}{3}

           P\left ( B \right )=P  (B hits target) =\frac{2}{5}

 

Solution: As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e. P\left ( A\cap B \right )=P\left ( A \right )P\left ( B \right )

            P\left ( A \cup B \right )=P(target will be hit by either A or B)

            \begin{aligned} P(A \cup B) &=P(A)+P(B)-P(A \cap B) \\ P(A \cup B) &=P(A)+P(B)-P(A) P(B) \\ &=\frac{1}{3}+\frac{2}{5}-\frac{1}{3} \times \frac{2}{5} \\ &=\frac{5+6-2}{15} \\ &=\frac{9}{15} \\ &=\frac{3}{5} \end{aligned}

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