SOLUTION: the probability of sunny weather on a day in cape town is 1/5 and the probability of wet weather is 1/4. Are the two events a. complementary? b. mutually exclusive? and/or c.

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Question 1175715: the probability of sunny weather on a day in cape town is 1/5 and the probability of wet weather is 1/4. Are the two events
a. complementary?
b. mutually exclusive? and/or
c. Disjointed events?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the probability of sunny weather on a day in cape town is 1%2F5+and the probability of wet weather is 1%2F4.

check if events are complementary:
The events of one outcome happening and that outcome not happening. The sum of the probabilities of an event and its complement is 1 or 100%
1/5+1/4=9/20=> 1/5+1/4<>1, so events are+not+complementary

check if events are mutually exclusive events:
Mutually exclusive events, also called disjoint events, are two or more outcomes of an event that cannot occur at the same time.
Another way to think of it is that two mutually inclusive events cannot happen independently. If you have two events that are dependent in some way, they are mutually inclusive.
In probability terms, two events are mutually inclusive if their intersection is greater than zero.
so, sunny weather and wet weather cannot occur at the same time but their intersection is+zero
->events are not mutually exclusive

check if events are disjoint: Events that cannot happen at the same time. In other words, they are mutually exclusive.
Put in formal terms, events A and B are disjoint if their intersection is zero.
Examples of disjoint events:
A football game can’t be held at the same time as a rugby game on the same field.
Heading East and West at the same time is impossible.
Tossing a coin and getting a heads and a tails at the same time is impossible.
You can’t take the bus and the car to work at the same time.
You can’t get a pay raise and a pay decrease at the same time.
->sunny weather and wet weather are disjoint events

so, answer is: c. disjoint events