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. 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 black and white or color? 0.06 0.07 0.13 0.26

Answer 1

To find the probability that a randomly selected participant dreams in black and white or color, we need to determine the probability of the union of events B and C. The probability can be calculated using the formula P(B ∪ C) = P(B) + P(C) - P(B ∩ C). Substituting the given values, the probability is 2/200 = 0.01 or 1%.

Step-by-step explanation:

To find the probability that a randomly selected participant dreams in black and white or color, we need to determine the probability of the union of events B and C.

We know that P(B) = 4, P(C) = 10, P(B ∩ C) = 12, and the total number of participants surveyed is 200.

The probability of dreaming in black and white or color can be calculated using the formula:

P(B ∪ C) = P(B) + P(C) - P(B ∩ C)

Substituting the given values, we get:

P(B ∪ C) = 4 + 10 - 12 = 2

The probability that a randomly selected participant dreams in black and white or color is 2/200 = 0.01 or 1%.