AMU 2026 — Mathematics PYQ

1. Understand the Formula

We are asked to find the conditional probability of $A$ given that $B$ does not occur ($\bar{B}$). The formula for conditional probability is:

$$P(A|\bar{B})=\frac{P(A\cap \bar{B})}{P(\bar{B})}$$

2. Calculate Necessary Components

• Find $P(\bar{B})$: The probability of the complement of event $B$ is:

  $$P(\bar{B})=1-P(B)=1-0.3=0.7$$

• Find $P(A\cap \bar{B})$:

  Using set theory, the area of $A$ that does not overlap with $B$ is the total probability of $A$ minus the intersection of $A$ and $B$:

  $$P(A\cap \bar{B})=P(A)-P(A\cap B)$$

  $$P(A\cap \bar{B})=0.5-0.15=0.35$$

3. Final Calculation

Now, substitute these values back into the conditional probability formula:

$$P(A|\bar{B})=\frac{0.35}{0.7}$$

To simplify this fraction:

$$P(A|\bar{B})=\frac{35}{70}=\frac{1}{2}=0.5$$

Conclusion

The value of $P(A|\bar{B})$ is 0.5. This result also highlights that $A$ and $B$ are independent events, since $P(A|\bar{B})=P(A)=0.5$.

This directly matches option (c).