Question

please answer question number 10

10. (Ch. 7) Sixty men out of 1,000 and three women out of 1,000 are color blind. A person is picked at random from a group containing 10 men and 10 women. (a) What is the probability that the person is color blind? (b) What is the probability that the person is a men if the chosen person is color blind? (c) Are gender and being color blind independent? 11. (Ch. 7) Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court judges consist of 23 men and 4 women (a) In how may ways can the two openings be filled? (b) What is the probability that both appointees are men? (c) What is the probability that exactly one woman is appointed?

Answer 1

Sixty men out of 1000 and three women out of 1000 are color blind. The number of men in 10 men who are color blind are 0.6 and the number of women in 10 men who are color blind are 0.03. Therefore, (a) The probability that a person is color blind in a group containing 10 men and 10 women is given as 0.6 + 0.03/20 = 0.63/20 = 0.0315 (b) Since the chosen person is color blind, there after, the probability that the person is man is given as 0.6/0.63 = 0.95 (correct to 2 decimal places (c) Given the person is color blind the probability that a person is man is different from the probability that the person is woman. Hence, gender and being color blind are not independent. (a) Since there are 27 judges i.e. 23 men and 4 women, so the 2 openings can be filled in ^27 c_2 ways i.e. 27!/25! times 2! = 27 times 26/2 = 27 times 13 = 351 \r\n