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Liula [17]
3 years ago
13

A civics teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the othe

r was true, but the students did not know this. The probability that a student selected at random believed the true headline was 90\%90%90, percent and the probability that the student believed the false headline was 82\%82%82, percent. She found that 75\%75%75, percent of the students believed both headlines.
Mathematics
1 answer:
dusya [7]3 years ago
8 0

Answer:

The events are not mutually exclusive.

Step-by-step explanation:

To determine that in the sample, are the events "believed the false headline" and "believed the true headline" mutually exclusive.

For two events, let say E₁ and E₂ are said to be mutually exclusive if they cannot both occur simultaneously. In set-theoretical notation, we can say that the two sets  E₁ and E₂ are disjoint. i.e.  E₁ ∩  E₂ = ∅ and the probability of them occurring at the same time is zero. i.e. Pr(  E₁ ∩  E₂ ) = 0

So, we can say;

Let P(true) = E₁  

P(false) = E₂

Thus; statistically:

Pr(  E₁ ∩  E₂ ) = Pr(E₁) + Pr(E₂) - P( E₁  ∪ E₂ )

So;

the probability of students that believed the true headline P(E₁) = 0.90

the probability of students that believed the false headline P(E₁) = 0.82

the probability of students that believed both P( E₁  ∪ E₂ ) = 0.75

∴

Pr(  E₁ ∩  E₂ ) = 0.90 + 0.82 - 0.75

Pr(  E₁ ∩  E₂ ) = 0.97

Thus, the events are not mutually exclusive.

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