True statement A and true statement | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\mathrm{P}(\mathrm{A})=0.3$

$\mathrm{P}(\mathrm{A} \vee \mathrm{B})=\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\math

Vedclass · Accepted Answer

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

Vedclass · Answer

$\mathrm{P}(\mathrm{A})=0.3$

$\mathrm{P}(\mathrm{A} \vee \mathrm{B})=\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})$

$\Rightarrow 0.8=0.3+\mathrm{P}(\mathrm{B})-0.3 \mathrm{P}(\mathrm{B})$

$\Rightarrow P(B)=\frac{5}{7}$

$ \mathrm{P}(\mathrm{A} ightarrow \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 	imes \frac{2}{7}ight)=\frac{32}{35} $

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)

Similar Questions

One card is drawn from a pack of $52$ cards. The probability that it is a queen or heart is

The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occurs simultaneously is $0.16$. Then the probability that none of the two occurs is

One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $\mathrm{E}$ and $\mathrm{F}$ independent ?

$E:$ ' the card drawn is a king and queen '

$F:$ ' the card drawn is a queen or jack '

Given two independent events $A$ and $B$ such $P(A)=0.3,\, P(B)=0.6 .$ Find $P(A $ and not $B)$

Let $A$ and $B$ be events for which $P(A) = x$, $P(B) = y,$$P(A \cap B) = z,$ then $P(\bar A \cap B)$ equals

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)