Question

Set $S$ has $4$ elements, $A$ and $B$ are subsets of $S$. The probability that$A$ and $B$ are not disjoint is

• A. $\frac{175}{256}$
• B. $\frac{173}{256}$
• C. $\frac{85}{128}$
• D. $\frac{45}{64}$

Answer 1

The correct option is A $\frac{175}{256}$

Total subsets of $S=2^4=16$

Total combination of $A$ & $B=16\times 16$

$=256$

Total $d$ is joints combinations of $A$ and $B=3^4$

$=81$

Probability that $A$ and $B$ are not $d$ is joint $=\frac{256-81}{265}$

$=\frac{175}{256}$

$A$ is correct