QJEEM24Ma162c: JEE Main 2024 Mathematics - Class 12 JEEM24Ma162c Solution: An integer is chosen at random from the integers . The…

Given set $=\{1,2,3, \ldots \ldots . .50\}$

$\mathrm{P}(\mathrm{A})=$ Probability that number is multiple of 4

$\mathrm{P(B)}=$ Probability that number is multiple of 6

$\mathrm{P}(\mathrm{C})=$ Probability that number is multiple of 7

Now,

$\mathrm{P}(\mathrm{A})=\frac{12}{50}, \mathrm{P}(\mathrm{B})=\frac{8}{50}, \mathrm{P}(\mathrm{C})=\frac{7}{50}$

again

$\begin{aligned}& \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{4}{50}, \mathrm{P}(\mathrm{B} \cap \mathrm{C})=\frac{1}{50}, \mathrm{P}(\mathrm{A} \cap \mathrm{C})=\frac{1}{50} \\& \mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=0\end{aligned}$

Thus

$\begin{aligned}P(A & \cup B \cup C)=\frac{12}{50}+\frac{8}{50}+\frac{7}{50}-\frac{4}{50}-\frac{1}{50}-\frac{1}{50}+0 \\& =\frac{21}{50}\end{aligned}$