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. A Venn Diagram titled Student Dreams. One circle is labeled B, 4, the other circle is labeled C, 10, the shared area is labeled 12, and the outside area is labeled 174. What is the probability that a randomly selected participant dreams in color only?
0.02
0.05
0.10
0.11
ANSWER:
0.05
In this Venn diagram, the probability that a randomly selected participant dreams in color only is equal to the proportion of participants who only dream in color, which is represented by the region labeled "C" in the Venn diagram. The probability is calculated by dividing the number of participants who only dream in color (10) by the total number of participants surveyed (200). Therefore, the probability is 0.05, or 5%.
To calculate the probability that a randomly selected participant dreams in both black and white and in color, we can add the number of participants in the shared region (12) to the number of participants who only dream in color (10), and divide by the total number of participants surveyed (200). This probability would be 0.14, or 14%.
