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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability Exercise 30.4 Question 19 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability  Exercise 30.4 Question 19 Maths Textbook Solution.

Answers (1)

Answer:  i. \frac{52}{77}     ii. \frac{25}{77}

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

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

Given: The odds against event A are 5 to 2. The odds in flavor of event B are 6 to 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.\begin{aligned} P(A \cap B) &=P(A)P(B)\end{aligned}

The odds against event A are 5 to 2.

                P(A)=\frac{\text { no.of outcome }}{\text { total outcome }}=\frac{2}{5+2}=\frac{2}{7}

The odds in flavor of event B are 6 to 5

                    P(B)=\frac{\text { no.of outcome }}{\text { total outcome }}=\frac{6}{6+5}=\frac{6}{11}         

  1. Probability of atleast one of the event occurs\Rightarrow

            \begin{aligned} P(A \cup B) &=P(A)+P(B)-P(A \cap B) \\ &=\frac{2}{7}+\frac{6}{11}-\frac{2}{7} \times \frac{6}{11} \\ &=\frac{22+42-12}{77} \\ &=\frac{52}{77} \end{aligned}

     ii   P(none of the event occurred) =1-P\left ( A\cup B \right )

                                                                    =1-\frac{52}{77}

                                                                    =\frac{25}{77}

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