If A and B are independent events such t

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

If A and B are independent events such that P(A) = 0.3, $P(A \cup \bar{B})$= 0.8, then P(B) equals to

Options:

$\frac{1}{7}$

$\frac{2}{7}$

$\frac{3}{4}$

$\frac{1}{4}$

Correct Answer:

$\frac{2}{7}$

Explanation:

$P(A)+P(\bar{B})-P(A) P(\bar{B})=0.8$

$0.3+(1-x)-0.3(1-x)=0.8$

$(1-x)(0.7)=0.5$

$1-x=\frac{5}{7} \Rightarrow x=1-\frac{5}{7}=\frac{2}{7}$