Questions: Color-Blind (C) Not Color-Blind (C) Total --------- Male (M) 72 64 136 Female (F) 19 35 54 Total 91 99 190 A person is randomly selected. What is the probability that the person is: a) Male? b) Male and Color-blind? c) Male given that the person is Color-blind? d) Color-blind given that the person is Male? e) Female given that the person is not Color-blind? f) Are the events Male and Color blind independent? Enter yes or no.

Solution Steps

To solve the given probability questions, we will use the data from the table to calculate the required probabilities.

a) To find the probability that a person is male, divide the total number of males by the total number of people.

b) To find the probability that a person is both male and color-blind, divide the number of color-blind males by the total number of people.

c) To find the probability that a person is male given that the person is color-blind, use the conditional probability formula: divide the number of color-blind males by the total number of color-blind people.

To find the probability that a randomly selected person is male, use the formula:

\[ P(\text{Male}) = \frac{\text{Total Males}}{\text{Total People}} = \frac{136}{190} \approx 0.7158 \]

To find the probability that a randomly selected person is both male and color-blind, use the formula:

\[ P(\text{Male and Color-Blind}) = \frac{\text{Color-Blind Males}}{\text{Total People}} = \frac{72}{190} \approx 0.3789 \]

To find the probability that a person is male given that the person is color-blind, use the conditional probability formula:

\[ P(\text{Male} \mid \text{Color-Blind}) = \frac{\text{Color-Blind Males}}{\text{Total Color-Blind}} = \frac{72}{91} \approx 0.7912 \]

Final Answer