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  • Explain Solution R.D. Sharma Class 12 Chapter 30 Probability Exercise Multiple Choice Questions Question 54 Maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 30 Probability  Exercise Multiple Choice Questions  Question 54 Maths Textbook Solution.

Answers (1)

Answer:(b)

Hint: You must know the rules of finding probability.

Given:P(A \cup B)=\frac{5}{9} \text { and } P(\bar{A} \cup \bar{B})=\frac{2}{3}

Solution:

\begin{aligned} &P(A \cup B)=\frac{5}{9} \\ &P(\bar{A} \cup \bar{B})=\frac{2}{3} \\ &P(\overline{A \cap B})=\frac{2}{3} \\ &1-P(A \cap B)=\frac{2}{3} \\ &P(A \cap B)=1-\frac{2}{3} \\ &=\frac{1}{3} \end{aligned}

Also,

\begin{aligned} &P(A \cup B)=P(A)+P(B)-P(A \cap B) \\ &=P(A)+P(B)=P(A \cup B)+P(A \cap B) \\ &P(A)+P(B)=\frac{5}{9}+\frac{1}{3} \\ &P(A)+P(B)=\frac{8}{9} \end{aligned}

Now,

\begin{aligned} &P(\bar{A})+P(\bar{B})=1-P(A)+1-P(B) \\ &=2-[P(A)+P(B)] \\ &=2-\frac{8}{9} \\ &=\frac{18-8}{9} \\ &=\frac{10}{9} \end{aligned}

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