Let $S=\{1,2,3, \ldots, 2022\}$. Then the probability, that a randomly chosen number $n$ from the set $S$ such that $\operatorname{HCF}( n , 2022)=1$, is.
Let $S=\{1,2,3, \ldots, 2022\}$. Then the probability, that a randomly chosen number $n$ from the set $S$ such that $\operatorname{HCF}( n , 2022)=1$, is.
- [JEE MAIN 2022]
- A
$\frac{128}{1011}$
- B
$\frac{166}{1011}$
- C
$\frac{127}{337}$
- D
$\frac{112}{337}$
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If $E$ and $F$ are independent events such that $0 < P(E) < 1$ and $0 < P\,(F) < 1,$ then
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- [IIT 1989]
Probability of solving specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that the problem is solved.
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If $A$ and $B$ are two events such that $P(A) = 0.4$ , $P\,(A + B) = 0.7$ and $P\,(AB) = 0.2,$ then $P\,(B) = $
If $A$ and $B$ are two events such that $P(A) = 0.4$ , $P\,(A + B) = 0.7$ and $P\,(AB) = 0.2,$ then $P\,(B) = $
Fill in the blanks in following table :
$P(A)$
$P(B)$
$P(A \cap B)$
$P (A \cup B)$
$\frac {1}{3}$
$\frac {1}{5}$
$\frac {1}{15}$
........
Fill in the blanks in following table :
| $P(A)$ | $P(B)$ | $P(A \cap B)$ | $P (A \cup B)$ |
| $\frac {1}{3}$ | $\frac {1}{5}$ | $\frac {1}{15}$ | ........ |