Question

The 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 ffour girls girls and no boys boys.

Answer 1

Answer:

The probability of four girls is:

$\dfrac{1}{16}$

Step-by-step explanation:

The sample space for 4 children consist of 16 entries and is given by:

{bbbb,bbbg,bbgb,bgbb,gbbb,bbgg,bgbg,ggbb,gbbg,gggg,gggb,ggbg,gbgg,bggg,gbgb,bggb}

i.e. The total number of outcomes=16.

Now the number of outcomes of getting four girls or we can say no boys=1=Number of favourable outcomes {i.e. the outcome is gggg}

Hence,

The probability of getting four girls= (Number of favourable outcomes)/(Total number of outcomes)=1/16

Hence, the probability of four girls is: $\dfrac{1}{16}$

Answer 2

The answer is 1/2^4 which 1/16 or 0.0625. there are 16 ways of getting either a girl or a boy in a limited order.