Question

In a population, 60 percent of the people are male and 40 percent are female. According to a report, 1.69 percent of all females are color blind and 8.73 percent of all males are color blind. What is the probability that a person randomly chosen from the population will be color blind? (Enter the answer upto three decimal accuracy)

Answer 1

Given : 60 percent of the people are male and 40 percent are female.

1.69 percent of all females are color blind and 8.73 percent of all males are color blind

To Find :probability that a person randomly chosen from the population will be color blind

Solution:

Let say population = 100P

Male = (60/100)100P = 60P

Female = (40/100)100P = 40P

1.69 percent of all females are color blind

=> Color blind female = (1.69/100)*40P  = 0.676P

8.73 percent of all males are color blind

=> Color blind female = (8.73/100)*60P  = 5.238P

Total Color blind =  0.676P + 5.238P  = 5.914P

probability that a person randomly chosen from the population will be color blind =  5.914P/100P

= 0.05914

= 0.059

Direct method

probability that a person randomly chosen from the population will be color blind =   (1.69/100)(40/100) + (8.73/100)(60/100)

= 0.05914

= 0.059

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Answer 2

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0.059 %✓