Probability 2 Question 7
7. Two events $A$ and $B$ have probabilities 0.25 and 0.50 , respectively. The probability that both $A$ and $B$ occur simultaneously is 0.14 . Then, the probability that neither $A$ nor $B$ occurs, is
(a) 0.39
(b) 0.25
(c) 0.11
(d) None of these
Objective Questions II
(One or more than one correct option)
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Answer:
Correct Answer: 7. (c)
Solution:
- Given, $P(A)=0.25, P(B)=0.50, P(A \cap B)=0.14$
$$ \therefore \quad P(A \cup B)=P(A)+P(B)-P(A \cap B) $$
$$ =0.25+0.50-0.14=0.61 $$
Now, $P(\overline{A \cup B})=1-P(A \cup B)=1-0.61=0.39$
