If A and B are two events. The probability that at most one of A, B occurs, is |
$1-P (A ∩ B)$ $P(\overline{A})+P(\overline{B})-P(\overline{A}∩\overline{B})$ $P(\overline{A})+P(\overline{B})+P(A ∪ B)-1$ all the above |
all the above |
We have, Required probability $=P(\overline{A}∪\overline{B})= P(\overline{A ∪ B})= 1- P (A ∩ B)$ So, alternative (a) is correct. Again $P(\overline{A}∪ \overline{B})=P(\overline{A})+P(\overline{B})-P(\overline{A}∩ \overline{B})$ [By add. Theorem] So, alternative (b) is correct. Again, $P(\overline{A}∪ \overline{B})$ $=P(\overline{A})+P(\overline{B})-P(\overline{A}∩ \overline{B})$ $=P(\overline{A})+P(\overline{B}) -P(\overline{A ∪ B})$ $=P(\overline{A})+P(\overline{B}) - \begin{Bmatrix}1- P(A ∪ B) \end{Bmatrix}$ $=P(\overline{A})+P(\overline{B}) + P(A ∪ B)-1$ So, alternative (c) is also correct. |