True statement A and true statement B are two independent events of an exper

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14.Probability

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True statement $A$ and true statement $B$ are two independent events of an experiment.Let $P\left( A \right) = 0.3$ , $P\left( {A \vee B} \right) = 0.8$ then $P\left( {A \to B} \right)$ is (where $P(X)$ denotes probability that statement $X$ is true statement)

$\frac{{32}}{{35}}$

$\frac{6}{{35}}$

$\frac{3}{{35}}$

data is insufficient

Solution

$\mathrm{P}(\mathrm{A})=0.3$

$\mathrm{P}(\mathrm{A} \vee \mathrm{B})=\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})$

$\Rightarrow 0.8=0.3+\mathrm{P}(\mathrm{B})-0.3 \mathrm{P}(\mathrm{B})$

$\Rightarrow P(B)=\frac{5}{7}$

$ \mathrm{P}(\mathrm{A} \rightarrow \mathrm{B}) =1-\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}}) $

$=1-(\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})) $

$=1-\left(0.3 \times \frac{2}{7}\right)=\frac{32}{35} $

Standard 11

Mathematics

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Solution

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True statement $A$ and true statement $B$ are two independent events of an experiment.Let $P\left( A \right) = 0.3$ , $P\left( {A \vee B} \right) = 0.8$ then $P\left( {A \to B} \right)$ is (where $P(X)$ denotes probability that statement $X$ is true statement)