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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 30 Probaility Exercise 30.4 Question 7 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 30 Probaility  Exercise 30.4 Question 7 Maths Textbook Solution.

Answers (1)

Answer: 0.77

Hint: P\left ( A \right )+P\left ( \bar{A} \right )=1

Given,

         P\left ( \bar{B}\right ) =0.65   

          P\left ( A\cup B \right )=0.85       

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 )

\begin{aligned} P(B) &=1-P(\bar{B}) \\ &=1-0.65 \\ &=0.35 \\ \end{aligned}

Now,

\begin{aligned} P(A \cup B)=P(A)+P(B)-P(A \cap B) \\ \end{aligned}

\begin{aligned} 0.85 &=P(A)[1-P(B)]+P(B) \\ 0.85 &=P(A) P(\bar{B})+0.35 \\ 0.85 &-0.35=P(A) \times 0.65 \\ \frac{0.50}{0.65} &=P(A) \\ P(A) &=\frac{10}{13} \\ &=0.77 \end{aligned}

                

                 

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