Consider a single spin of the spinner.
2 answers:
The question is incomplete
Find attached to the question, the appropriate diagram
Answer:
a) landing on an unshaded sector and landing on a number less than 2
b) landing on a shaded sector and landing on a 3
Step-by-step explanation:
Mutually exclusive events are two events that can occur separately on their own but they cannot occur together or at the same time.
The options given are explained below:
We have two shaded sectors: 1 and 4
We have two unshaded sectors : 2 and 3
a) landing on an unshaded sector and landing on a number less than 2
Looking at option a, we find out that it is possible for the spinners to land on an unshaded sector separately likewise on a number less than 2 but it cannot land on an unshaded sector AND and number less than 2 because looking at the spinner, the numbers on the unshaded sectors are 2 ( is equal to two) and 3 ( which is above 2).
Therefore this option is mutually exclusive and correct.
b) landing on a shaded sector and landing on a 3
It is possible to land on a shaded sector likewise it is possible to land on a 3 but it is not possible to land on a shaded sector and land on a 3 at the same time.
This is because, the number on the shaded sector is 1 and 4 and the number on the unshaded sector is 2 and 3, we have only one spinner so the spinner can only land on one sector at a time.
Therefore, Option b is a mutually exclusive event and it is a correct option.
c) landing on an unshaded portion and landing on an odd number
The unshaded portion on the spinner has number 2 and 3 on them, therefore it is possible to land on an unshaded portion and odd number which is 3 at the same time.
Option c is not a mutually inclusive event and it is wrong.
d) landing on a shaded sector and landing on an even number
The shaded sector on the spinner has number 1 and 4 on them, therefore it is possible to land on an shaded sector and even number which is 4 at the same time.
Option d is not a mutually inclusive event and it is wrong.
e)landing on a shaded sector and landing on a number greater than 3
The shaded sector on the spinner has number 1 and 4 on them, therefore it is possible to land on an shaded sector and a number greater than 3 which is 4 at the same time.
Option e is not a mutually inclusive event and it is wrong.
Therefore, option a and option b are mutually exclusive events and they are correct.
Answer:
a. landing on an unshaded sector and landing on a number less than 2
e landing on a shaded sector and landing on a number greater than 3
Step-by-step explanation:
Two events ; for example events A and B are said to be mutually exclusive , if they cannot both occur simultaneously.In set theoretical notation , we say that the two sets A and B are disjoint set.
i.e
A ∩ B = ∅
Pr (A ∩ B) = 0
The intersection of A and B is an empty set and as such there is no intersection.
From the given options; option a and e are correct because ;
a.
landing on an unshaded sector and landing on a number less than 2
Landing on an unshaded portion would 2 or 3.
Landing on a number less than 2 would be 1.
There is no intersection and as such these events are mutually exclusive.
e.
landing on a shaded sector and landing on a number greater than 3
Landing on a shaded portion would be 1 or 4.
Landing on a number greater than 3 would be just 4.
The intersection of both events will be an empty set (∅)
As such these events are not mutually exclusive.
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