Question

Teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the other was true, but the students did not know this. The probability that a student selected at random believed the true headline was 90% and the probability that the student believed the false headline was 82%. She found that 75% of the students believed both headlines.

In this sample, are the events 'believed the false headline' and 'believed the true headline' mutually exclusive?

Choose 1 answer:

Yes
No
Find the probability that a randomly selected person from this sample believed the true headline OR believed the false headline.

P (believed true OR believed false) =?

Answer 1

The events in question are not mutually exclusive since a student can believe both headlines. The probability that a student believes at least one of the headlines is 97%.

Step-by-step explanation:

The events 'believed the false headline' and 'believed the true headline' are not mutually exclusive, as it's possible for students to believe both headlines. To calculate the probability that a randomly selected person believed either the true headline or the false headline, you can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

So:

P(believed true OR believed false) = P(believed true) + P(believed false) - P(believed both)

= 0.90 + 0.82 - 0.75

= 0.97 or 97%

This is the probability that a student believes at least one of the headlines.