Question

students majoring in psychology surveyed 200 of their fellow students about their dreams. the results of the survey are shown in the venn diagram. let b be the event that the participant dreams in black and white and let c be the event that the participant dreams in color.
what is the probability that a randomly selected participant dreams in black and white or color?
0.06
0.07
0.13
0.26
student dreams

Explanation:

Step1: Calculate the number of participants who dream in black and white or color

The formula for \(n(B\cup C)\) is \(n(B\cup C)=n(B - C)+n(C - B)+n(B\cap C)\).
Here, \(n(B - C) = 4\), \(n(C - B)=10\), \(n(B\cap C)=12\).
So, \(n(B\cup C)=4 + 10+12=26\).

Step2: Calculate the probability

The probability \(P(B\cup C)=\frac{n(B\cup C)}{n(\text{total})}\).
Since \(n(\text{total}) = 200\), then \(P(B\cup C)=\frac{26}{200}=0.13\).

Answer:

\(0.13\) (the third option)