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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability Exercise 30.4 Question 20 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability  Exercise 30.4 Question 20 Maths Textbook Solution.

Answers (1)

Answer: \frac{7}{8}

Hint: P(A \cup B \cup C)=P(A)+P(B)+P(C)-[P(A \cap B)+P(B \cap C)+P(C \cap A)]+P(A \cap B \cap C)

Given: A die is thrown thrice. Find the probability of getting an odd number at least once.

Solution:

P (Getting an odd number in one throw) =\frac{3}{6}=\frac{1}{2} …{there are 3 odd numbers in an throw of a dice}

Here, getting an odd number in three throws refers to 3 independent events

                       P\left ( A \right )=P\left ( B \right )=P\left ( C \right )=\frac{1}{2}

        P(A \cup B \cup C)=P(A)+P(B)+P(C)-[P(A \cap B)+P(B \cap C)+P(C \cap A)]+P(A \cap B \cap C)

                                   \begin{aligned} &=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}-\left[\frac{1}{2} \times \frac{1}{2}+\frac{1}{2} \times \frac{1}{2}+\frac{1}{2} \times \frac{1}{2}\right]+\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \\ &=\frac{12-6+1}{8} \\ &=\frac{7}{8} \end{aligned}

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