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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 30 Probaility Exercise 30.5 Question 16 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 30 Probaility  Exercise 30.5 Question 16 Maths Textbook Solution.

Answers (1)

Answer:\frac{107}{120}

Hint: You must know the rules of finding probability.

Given:  A speaks truth three times out of four

B speaks truth four times out of five

C speaks truth five times out of six

Solution:P\left ( A\: Speaks\: truth \right )=\frac{3}{4}

P\left ( B\: Speaks\: truth \right )=\frac{4}{5}

P\left ( C\: Speaks\: truth \right )=\frac{5}{6}

\begin{aligned} &P \text { (majority speaks truth) }=P \text { (two speak truth) }+P(\text { all speak truth }) \\ \end{aligned}

\begin{aligned} &=P(A) \times P(B)[1-P(C)]+P(A) \times P(C)[1-P(B)] \\ \end{aligned}\begin{aligned} &+P(C) \times P(B)[1-P(A)]+P(A) \times P(B) P(C) \\ \end{aligned}\begin{aligned} &+P(C) \times P(B)[1-P(A)]+P(A) \times P(B) P(C) \\ \end{aligned}

\begin{aligned} &=\frac{3}{4} \times \frac{4}{5}\left(1-\frac{5}{6}\right)+\frac{3}{4} \times \frac{5}{6}\left(1-\frac{4}{5}\right)+\frac{4}{5} \times \frac{5}{6}\left(1-\frac{3}{4}\right)+\frac{3}{4} \times \frac{4}{5} \times \frac{5}{6} \\ &=\frac{12}{120}+\frac{15}{120}+\frac{20}{120}+\frac{60}{120} \\ &=\frac{107}{120} \end{aligned}

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