Question

The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then $P \left( A ^ { \prime } \right) + P \left( B ^ { \prime } \right) =$

• A. 0.9
• B. 1.15
• C. 1.1
• D. 1.2

Answer 1

Answer: (C)

1.1

Answer 2

$1 - P \left( A ^ { \prime } \cap B ^ { \prime } \right) = 0.6$ $P ( A \cap B ) = 0.3$ then

$P \left( A ^ { \prime } \cup B ^ { \prime } \right) = P \left( A ^ { \prime } \right) + P \left( B ^ { \prime } \right) - P \left( A ^ { \prime } \cap B ^ { \prime } \right)$

⇒ $1 - P ( A \cap B ) = P \left( A ^ { \prime } \right) + P \left( B ^ { \prime } \right) - 0.4$

⇒ $P \left( A ^ { \prime } \right) + P \left( B ^ { \prime } \right) = 0.7 + 0.4 = 1.1$ .