2. Two mark example problems

1. If \(P(A) = 0.37\), \(P(B) = 0.42\), \(P(A \cap B) = 0.09\) then find \(P(A \cup B)\).

 

Answer:

 

\(P(A \cup B) =\)

 

2. What is the probability of drawing either a king or a queen in a single draw from a well shuffled pack of \(52\) cards?

 

Answer:

 

The probability of drawing either a king or a queen \(=\) $\frac{i}{i}$.

 

3. If \(A\) and \(B\) are two events such that \(P(A) = \frac{1}{4}\), \(P(B) = \frac{1}{2}\) and \(P(A \ \text{and} \ B) = \frac{1}{8}\), find (i) \(P(A \ \text{or} \ B)\) (ii) \(P(\text{not} \ A \text{and not} \ B)\).

 

Answer:

 

(i) \(P(A \ \text{or} \ B) = \) $\frac{i}{i}$

 

(ii) \(P(\text{not} \ A \text{and not} \ B) =\) $\frac{i}{i}$

 

 

4. \(A\) and \(B\) are two candidates seeking admission to IIT. The probability that \(A\) getting selected is \(0.5\) and the probability that both \(A\) and \(B\) getting selected is \(0.3\). Prove that the probability of \(B\) being selected is atmost \(0.8\).

 

Answer:

 

The given statement is FalseTrue.