Question

Nine percent of all people cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals. Six drivers are randomly selected for a study of traffic signal perceptions. What is the probability that the number of drivers with this type of color blindness is exactly two?

A. 0.374
B. 0.303
C. 0.500
D. 0.630

Answer 1

The probability of exactly two out of six drivers being colorblind can be calculated using the binomial probability formula. However, the calculated probability does not match any of the given options, suggesting there could be an error in the options provided or in the calculation.

Step-by-step explanation:

The student is asking about the probability of exactly two out of six drivers being colorblind given that nine percent of all people have red-green color blindness. To find this probability, we can use the binomial probability formula, which is P(X = k) = (n choose k) * pk * (1-p)(n-k), where 'n' is the number of trials (6 drivers), 'k' is the number of successes (2 drivers are colorblind), and 'p' is the probability of success on a single trial (0.09 or 9%).

Using the formula, we have:

P(X = 2) = (6 choose 2) * (0.09)2 * (0.91)4
= 15 * 0.0081 * 0.6859
= 0.08331

After calculating, 0.08331 does not exactly match any of the provided options (A, B, C, D). Thus, there might be a typo or mistake in the provided options or the calculation. The correct approach to the problem, however, uses the binomial probability formula as demonstrated.