Which of the terms i) overlapping ii) compound iii) mutually exclusive iv) permutation can be applied to the events described?
Suppose we have a colored dice. The events of interest are as follows
1) Rolling red or a primary color
2) Rolling orange or a primary color
3) Rolling two colored dice, rolling a yellow and then a green
Events are overlapping if the individual events can occur in combination.
A compound event is one where the outcome depends on two or more independent events.
Events are mutually exclusive if the events can only occur individually and cannot occur together.
Events are Independent if they do not depend on each other's outcome.
An event can permute if the independent events within the event can occur in a different order, or way.
1) Rolling a red or a primary colour:
Since red is a primary colour, we can roll a red and a primary colour
at once, or another primary colour other than red (ie yellow or blue).
The events are overlapping.
2) Rolling an orange or a primary colour:
Orange is not a primary colour, so either we roll orange or we roll
a primary colour (red, yellow or blue).
The events are mutually exclusive.
3) Rolling the cube twice - a yellow and then a green.
As long as the cube isn't weighted (ie not biased) then the second
roll is not affected by the first.
The events are independent. The combined event of rolling a yellow
and then a green is a compound event. If the yellow and green could
be rolled in any order then this would be a permutation of that
occurence (the other possible permuation is rolling green and then
1) The events are overlapping
2) The events are mutually exclusive
3) The events are independent and the combined event is a compound
event. The combined event may possibly be a permutation.
1. Overlapping Event
2. Mutually Exclusive Event
3. Independent Events