Question

a college professor asked his psychology students to complete a personality test. he paid special attention to his students career goals and their greatest fears. the probability that a student wants to be a psychologist is 0.8, and the probability that a student has a fear of public speaking is 0.5. what is the probability that a randomly chosen student wants to be a psychologist or has a fear of public speaking if those are independent events? write your answer as a whole number, decimal, or simplified fraction.

Explanation:

Step1: Recall the formula for the probability of the union of two independent events.

The formula for \( P(A \cup B) \) when \( A \) and \( B \) are independent events is \( P(A \cup B)=P(A)+P(B)-P(A)P(B) \), where \( A \) is the event that a student wants to be a psychologist and \( B \) is the event that a student has a fear of public speaking.

Step2: Substitute the given probabilities into the formula.

We know that \( P(A) = 0.8 \), \( P(B)=0.5 \). First, calculate \( P(A)P(B) \): \( 0.8\times0.5 = 0.4 \). Then, substitute into the formula for \( P(A \cup B) \): \( P(A \cup B)=0.8 + 0.5- 0.4 \).

Step3: Perform the arithmetic operations.

\( 0.8+0.5 = 1.3 \), and \( 1.3 - 0.4=0.9 \).

Answer:

\( 0.9 \)