JEE Main 2024 — Mathematics Probability & Statistics

Let $A={1,2,3,4,5,.........,50}$A=1,2,3,4,5,.........,50

Now, the probability of choosing a number which is a multiple of $4$4 will be $P(4)=\frac{12}{50}$P(4)=5012​

Similarly, the probability of choosing a number which is a multiple of $6$6 will be $P(6)=\frac{8}{50}$P(6)=508​

And the probability of choosing a number which is a multiple of $7$7 will be $P(7)=\frac{7}{50}$P(7)=507​

Also, the probability of choosing a number which is a multiple of 4&6 will be $P(4\cap 6)=\frac{4}{50}$P(4∩6)=504​

And the probability of choosing a number which is a multiple of 6&7 will be $P(6\cap 7)=\frac{1}{50}$P(6∩7)=501​

And the probability of choosing a number which is a multiple of 4&7 will be $P(4\cap 7)=\frac{1}{50}$P(4∩7)=501​

And finally, the probability of choosing a number which is a multiple of 4,6&7 will be $P(4\cap 6\cap 7)=0$P(4∩6∩7)=0

Hence, $P(4\cup 6\cup 7)=\frac{12}{50}+\frac{8}{50}+\frac{7}{50}-\frac{4}{50}-\frac{1}{50}-\frac{1}{50}+0$P(4∪6∪7)=5012​+508​+507​−504​−501​−501​+0

$$\Rightarrow P(4\cup 6\cup 7)=\frac{21}{50}$$⇒P(4∪6∪7)=5021​