Determine whether the events are disjoint.
-If $\mathrm { P } ( \mathrm { A } ) = \frac { 14 } { 15 }$, find $\mathrm { P } ( \overline { \mathrm { A } } )$
A) $\frac { 1 } { 15 }$
B) $\frac { 15 } { 14 }$
C) 0
D) $\frac { 14 } { 29 }$

Question

Quizplus · Accepted Answer

Two events are disjoint (or mutually exclusive) if they cannot occur at the same time. In this case, we are not given any information about another event that could occur with event A, so we assume that event A is the only possible event. Therefore, the probability of the complement of event A, which is the event that A does not occur, is equal to the probability of all other possible outcomes. Since the sum of the probabilities of all possible outcomes is 1, we have:

$$\mathrm { P } ( \overline { \mathrm { A } } ) = 1 - \mathrm { P } ( \mathrm { A } ) = 1 - \frac{14}{15} = \frac{1}{15}$$

Therefore, the best choice is A.

Determine Whether the Events Are Disjoint P(A)=1415\mathrm { P } ( \mathrm { A } ) = \frac { 14 } { 15 }P(A)=1514​

Determine Whether the Events Are Disjoint $\mathrm { P } ( \mathrm { A } ) = \frac { 14 } { 15 }$