a) A survey of a sample of business students resulted in the following information, regarding the...

Question:

a) A survey of a sample of business students resulted in the following information, regarding the genders of the individuals and their selected major:

male:
management: 40
marketing: 10
others: 30
total: 80

female:
management: 30
marketing: 20
others: 70
total: 120

What is the probability of selecting an individual, who is either male, or majoring in Management?

Non-Mutually Exclusive:

Mutually exclusive events are events that can't happen at the same time. Say we toss a coin once, then we know that the coin will fall either heads or tails but can't be both. On the other hand, non-mutually exclusive events are the events that can happen at the same time or have an overlap.

Answer and Explanation:

The problem asks for event A, male, or event B, majoring in management. The rule for "OR" when two events, {eq}A {/eq} and {eq}B {/eq}, are non-mutually exclusive is given by:

$$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) $$

The term {eq}P\left(A\cap B\right) {/eq} refers to the overlap of events {eq}A {/eq} and {eq}B {/eq}, that is, males who majored in management. And by looking at the data, we can see that there are {eq}40{/eq} of them. The total of all the individuals is {eq}80 + 120 = 200 {/eq}. Also, we can see that there are {eq}40{/eq} males and {eq}30{/eq} females who took management. Now, substituting values into the equation:

$$P\left(A\cup B\right)=\frac{80}{200}+\frac{40+30}{200}-\frac{40}{200} \\ P\left(A\cup B\right)= \frac{11}{20} $$

$$\boxed{P\left(A\cup B\right)= \frac{11}{20}} $$


Learn more about this topic:

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Mutually Exclusive Events & Non-Mutually Exclusive Events

from 6th-8th Grade Math: Practice & Review

Chapter 48 / Lesson 5
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