Genetics. What is the probability have at least 2 boys out of 4 children

the possible combinations of boys and girls are: bbbb bbbg bbgg bggg gggg all boys can occur in 1 way so p(4b) = 1 * .5^4 = .0625 3 boys 1 girl can occur in 4 ways so p(3b1g) = 4 * .5^4 = .25 2 boys 2 girls can occur in 6 ways so p(2b2g) = 6 * .5^4 = .375 1 boy 2 girls can occur in 4 ways so p(1b3g) = 4 * .5^4 = .25 all girls can occur in 1 way so p(4g) = 1 * .5^4 = .0625 sum of all probabilities should be equal to 1. 2 * .0625 2 * .25 .375 = 1 so we're good there. probability of at least 2 boys equals p(2b2g) p(3b1g) p(4b) = .375 .25 .0625 = .6875 = % the number of ways you can get all boys is 1 as shown below: bbbb the number of ways you can get 3 boys and 1 girls is 4 as shown below: bbbg bbgb bgbb gbbb the number of ways you can get 2 boys and 1 girl is 6 as shown below: bbgg bggb ggbb gbbg bgbg gbgb since the order in which the children arrive has something to do with the probability of them arriving, these would be permutations. since the probability of having a boy or a girl was the same (.5 in each case), the probability part of the equations was always the same (.5^4) regardless of whether it was 1 boy, 2 boys, 3 boys, or 4 boys. for example: p(bbbb) = .5*.5*.5*.5 = .5^4 p(gggg) = .5*.5*.5*.5 = .5^4 p(bbbg) = .5*.5*.5*.5 = .5^4 p(bbgg) = .5*.5*.5*.5 = .5^4 if the probability was different, i.e. p(b) = .75, p(g) = .25, then the probability for each of the permutations would have been different. for example: p(bbbb) = .25*.25*.25*.25 = .25^4 p(gggg) = .75*.75*.75*.75 = .75^4 p(bbbg) = .25*.25*.25*.75 = .25^3*.75 p(bbgg) = .25*.25*.75*.75 = .25^2*.75^2 #genomes #alleles #genes #Eukaryotes #GeneticsLecture #MolecularBiology #GeneticTesting #RNA #phenotype #GeneticExamQuestionsSolutions #geneExpression #gene #chromosome #geneticCode #Genetics101 #Proteins #GeneStructure #Genetics #genotype #DNA #NikolaysGeneticsLessons #simpleProbability #math #Statistics #chances #coinToss #probabilityLine #likelyEvent #unlikelyEvent #probability #introduction #sampleSpace #treeDiagrams #CrashCourse #crashcourse #independent #education