Find the probability of getting exactly 6 girls in 8 births.

Answer:The probability of getting exactly 6 girls in 8 births is 0.1093Step-by-step explanation:Given : 6 girls in 8 births.To find : The probability of getting exactly 6 girls in 8 births.Solution : The probability of getting girl is [tex]\frac{1}{2}[/tex]The probability of getting 6 girl is [tex](\frac{1}{2})^6[/tex]Since we have 6 girls, We also need to find the probability of getting 2 boys, which is  [tex](\frac{1}{2})^2[/tex]There are [tex]^8C_6[/tex] ways to get 6 girls in 8 births i.e, [tex]^8C_6=\frac{8!}{6!\times 2!}[/tex] [tex]^8C_6=\frac{8\times 7\times 6!}{6!\times 2\times 1}[/tex] [tex]^8C_6=28[/tex] There are 28 ways to get 6 girls in 8 births.The probability of getting exactly 6 girls in 8 births.[tex]=28\times (\frac{1}{2})^6\times (\frac{1}{2})^2[/tex][tex]=28\times 0.015625\times 0.25[/tex][tex]=0.109375[/tex]Therefore, The probability of getting exactly 6 girls in 8 births is 0.1093