Let $A$ and $B$ be independent events such that $\mathrm{P}(\mathrm{A})=\mathrm{p}, \mathrm{P}(\mathrm{B})=2 \mathrm{p} .$ The largest value of $\mathrm{p}$, for which $\mathrm{P}$ (exactly one of $\mathrm{A}, \mathrm{B}$ occurs $)=\frac{5}{9}$, is :

  • [JEE MAIN 2021]
  • A

    $\frac{1}{3}$

  • B

    $\frac{2}{9}$

  • C

    $\frac{4}{9}$

  • D

    $\frac{5}{12}$

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  • [IIT 2023]