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  • Need solution for RD sharma maths class 12 chapter 30 probablity exercise Very short answer question, question 15

Need solution for RD sharma maths class 12 chapter 30 probablity exercise Very short answer question, question 15

Answers (1)

The value of  P(A\cup B)=0.75

Hint:

Using the formula,

P(B | A) = \frac{P(A\cap B)}{P(A)}  first find P(A\cap B)

Then using the relation, P(A \cup B)=P(A)+P(B)- P(A\cap B),

Find the required value

Given:

P(A) = 0.3

P(B) = 0.6

P(B|A) = 0.5

Explanation:

We know ,

\begin{aligned} &P(B \mid A)=P(A \cap B) \\ &P(B / A)=\frac{P(A \cap B)}{P(A)} \\ \end{aligned}

\begin{aligned} &\Rightarrow 0.5=\frac{P(A \cap B)}{0.3} \\ &\Rightarrow P(A \cap B)=0.5 \times 0.3 \\ &\Rightarrow P(A \cap B)=0.15 \end{aligned}

We know ,

\begin{aligned} P(A \cup B) &=P(A)+P(B)-P(A \cap B) \\ &=0.3+0.6-0.15 \\ &=0.75 \end{aligned}

Hence , P(A\cup B)=0.75

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