JAMIA 2021 — Mathematics PYQ

• Probability that at least one of the events $A$ and $B$ occurs: $P(A\cup B)=0.6$

• Probability that $A$ and $B$ occur simultaneously: $P(A\cap B)=0.2$

2. Use the Addition Theorem of Probability

The formula for the union of two events is:

Substitute the given values into the formula:

Solve for $P(A)+P(B)$:

3. Relate Complements to the Probability

We know that for any event $E$, the probability of its complement is $P(\bar{E})=1-P(E)$.

So:

4. Calculate the Required Sum

We need to find $P(\bar{A})+P(\bar{B})$:

Substitute the value from equation (1):

Final Result

The value of $P(\bar{A})+P(\bar{B})$ is $1.2$.