Question

he sample space listing the eight simple events that are possible when a couple has three children is​ {bbb, bbg,​ bgb, bgg,​ gbb, gbg,​ ggb, ggg}. After identifying the sample space for a couple having four​ children, find the probability of getting one girl and three boys left parenthesis in any order right parenthesis. Identify the sample space for a couple having four children. ​{ nothing​} ​(Use a comma to separate answers as​ needed.) Find the probability of getting one girl and three boys left parenthesis in any order right parenthesis. nothing ​(Type an integer or a decimal. Do not​ round.)

Answer 1

Answer :

given data :-

a couple has three children = ( bbb, bbg,​ bgb, bgg,​ gbb, gbg,​ ggb, ggg )

now we need to find out the  probability of getting one girl and three boys left parenthesis in any order right parenthesis :

here,

sample space for 4 children is as may following are :

( bbbb ; bbbg ; bbgb ; bgbb ; gbbb ; bbgg ; bggb ; bgbg ; ggbb ; gbgb ; gbbg ;bggg ; gbgg ; ggbg ;gggb ;gggg )

total 16 outcomes.

total number of outcome with one girl and three boys

= ( bbbg ; bbgb ; bgbb ; gbbb )

= 4

hence,

probability of one girl and three boys

= 4/16

= 1/4

= 0.25

The probability of getting one girl and three boys left parenthesis in any order right parenthesis

= 0.25 (or) 1/4