A and B are two events such that \( \mathrm{P}(\mathrm{A})=0.25 \) and \( \mathrm{P}(\mathrm{B})=0.50 \). The probability of both happening together is 0.14. The probability of both A and B not happening is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.39
By the addition rule,
\( \displaystyle P(A\cup B)=0.25+0.50-0.14 \)
\( \displaystyle =0.61 \)
“Neither A nor B” is the complement of \( A\cup B \):
\( \displaystyle P(\bar{A}\cap\bar{B})=1-0.61 \)
\( \displaystyle =0.39 \)