Question 1194183: Determine whether the given events are mutually exclusive or not. Write M if mutually and N if not.
1. A die rolled once. What is the probability of getting a 2 or 4?
2. Tossing a coin. What is the probability of getting a head?
3. A box has 2 red balls, 4 white balls, and 7 blue balls. If a ball is drawn at a random from the box, what is the probability that it is red or blue
4. A die is rolled once. What is the probability of getting a 4 or a number divisible by 2?
i need this rn.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Problem 1
Definition: Mutually exclusive events are two (or more) events that cannot happen simultaneously.
Possibly a classic example would be getting heads AND tails on the same coin flip. Such a thing isn't possible.
If A and B are mutually exclusive events, then P(A and B) = 0, ie the probability of both events happening is 0
Let's define these two events
A = getting a 2 on a six-sided die
B = getting a 4 on a six-sided die
Hopefully you agree that A and B cannot happen at the same time for the same single die roll.
Therefore, these two events are mutually exclusive.
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Problem 2
The probability of getting heads is 1/2 since we have 1 side labeled "heads" out of 2 sides total.
1/2 = 0.50 = 50%
There isn't any other event to compare this with, so we cannot say "mutually exclusive" here. It doesn't make sense to do so. The only realistic answer is to write "N" for "not mutually exclusive". Even then it might be misleading. I would ask your teacher for clarification on this problem.
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Problem 3
I'm assuming the balls have 1 single color only.
If you pull one ball out, then there's no way to get red AND blue at the same time.
Therefore, the events "select red" and "select blue" are indeed mutually exclusive.
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Problem 4
Define these two events
A = rolling a 4
B = rolling a number divisible by 2
Is it possible for events A and B to happen at the same time? Yes it is.
The number 4 itself is divisible by 2 because 4 = 2*2
In other words, 2 is a factor of 4.
This means P(A and B) is not zero, which leads to A and B being not mutually exclusive.
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