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  • Provide solution for RD sharma maths class 12 chapter 30 Probablity Exercise very short answer question, question 7

Provide solution for RD sharma maths class 12 chapter 30 Probablity Exercise very short answer question, question 7

Answers (1)

 The value of P(B) is \frac{2}{7}

Hint:

P(A\cup B')=P(A)+P(B')-P(A\cap B') and

If A & B are independent then P(A\cap B)=P(A).P(B)

Given

P(A)=0.3\; \& \;P(A \cup B')=0.8

Explanation:

It is given that,

P(A)=0.3 \& \\ P(A\cup B')=0.8

We know,
P(A\cup B')= P(A)+ P(B') -P(A\cap B)' \\ \Rightarrow P(A\cup B') =P(A)+P(B')-P(A).P(B')\\ \Rightarrow 0.8 =0.3+P(B') - 0.3 . P(B')\\ \Rightarrow 0.5 =P(B')-0.3 P(B' )\Rightarrow P(B') =\frac{0.5}{0.7}=\frac{5}{7}              (since, A and B are Independent)

Also, we know,

P(B)=1-P(B')=1-\frac{5}{7}=\frac{2}{7}

Thus, P(B)=\frac{2}{7}

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