Okay my question is based on a previous question so let mefirst give you the org

Question

Okay my question is based on a previous question so let mefirst give you the orginal equation with the answers, so you canbetter understand my question at the bottom. A family has four children, all girls a.) constuct a sample space for the possible genders of fourchildren. Answer is (F,F,F,F), ( F,F,FM),(F,F,MF),(F,F,M,M),(F,M,F,F),(F,M,F,M),(F,M,M,F),(F,M,M.M),(M,M,M,M),(M,M,M,F),(M,F,M,M),(M,M,F,M),(M,M,F,F),(M,F,M,F),(M,F,F,M)and (M,F,F,F). B.) If each child is equally likely to be a girl ot boy, findthe probability that all four children are female. Now let me tell you the question I need help with. Refer to the previous exercise, What's wrong with thefollowing logic for part b( the part that says that the possibly ofhaving a male or female is equal)? A family with 4 children canhave 0,1,2,3, or 4 girls. Since there are five possibilities, theprobability of 4 girls is 1/5. Okay my question is based on a previous question so let mefirst give you the orginal equation with the answers, so you canbetter understand my question at the bottom. A family has four children, all girls a.) constuct a sample space for the possible genders of fourchildren. Answer is (F,F,F,F), ( F,F,FM),(F,F,MF),(F,F,M,M),(F,M,F,F),(F,M,F,M),(F,M,M,F),(F,M,M.M),(M,M,M,M),(M,M,M,F),(M,F,M,M),(M,M,F,M),(M,M,F,F),(M,F,M,F),(M,F,F,M)and (M,F,F,F). B.) If each child is equally likely to be a girl ot boy, findthe probability that all four children are female. Now let me tell you the question I need help with. Refer to the previous exercise, What's wrong with thefollowing logic for part b( the part that says that the possibly ofhaving a male or female is equal)? A family with 4 children canhave 0,1,2,3, or 4 girls. Since there are five possibilities, theprobability of 4 girls is 1/5.

Explanation / Answer

your logic is absolutely wrong. lets go step wise probability that the first child born is a girl = 0.5 (as in the question itself its given that each child is equallylikely to be a girl or boy) similarly, probability that the second child born is a girl =0.5 similarly, probability that the third child born is a girl =0.5 similarly, probability that the fourth child born is a girl =0.5 hence, the probability that all four children are female =0.5*0.5*0.5*0.5 = 0.0625

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