Answer

Verified

413.1k+ views

**Hint:**The probability of a situation is given by $\dfrac{\text{favourable outcome}}{ \text{total outcome}}$. So in order to get the required probability we’ll find how many cases are in our favour and how many total cases we have.

**Complete step by step solution:**Given, there are two families each having two children and at least two are girls among the children.

The total number of children in the families is 4.

Let us take the following cases:

Case I:

There are 2 girls and 2 boys in the families.

As we have to choose 2 boys thus we can choose in $^{4}C_{2}$ways.

Case II:

There are 3 girls and 4 boys in the family.

As we have to choose 1 boy thus we can choose in $^{4}C_{1}$ways.

Case III:

There are 4 girls and 0 boys in the families.

Thus we can choose in only 1 way.

The favourable outcome is 1.

The total outcome is ${1}+{}^{4}{C_{1}}+{}^{4}{C_{2}}$

The probability that all children are girls is

$\dfrac{1}{{1}+{}^{4}{C_{1}}+{}^{4}{C_{2}}}$

By simplifying using the formula ${}^n{C_r}=\dfrac{n!}{r! \times \left(n-r!\right)}$ the combination we get,

$\dfrac{1}{1+4+6}=\dfrac{1}{11}$

**Note:**In such a type of question we need to case several cases to find the total outcomes. Here at least 2 girls means 2 or more than 2. Counting the total number of cases correctly makes your half job done. Sometimes we take help from topics like permutation and combination to count the cases.

Recently Updated Pages

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

The provincial president of the constituent assembly class 11 social science CBSE

Gersoppa waterfall is located in AGuyana BUganda C class 9 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The hundru falls is in A Chota Nagpur Plateau B Calcutta class 8 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE