Question

Three groups of children contain respectively 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected from each group. The chance that the three selected children consists of one girl and two boys is:

1. $\dfrac{9}{{32}}$
2. $\dfrac{{11}}{{32}}$
3. $\dfrac{{13}}{{32}}$
4. $\dfrac{7}{{32}}$

Answer 1

In the above question we are supposed to find Probability of the given condition.
Probability is the prediction or we can say probability is the estimate of occurrence of an event. Probability in mathematical terms is given as the ratio of favorable outcome upon total outcome.
$P = \dfrac{{favorable\ out\ come}}{{total\ outcome}}$
Using the above formula we will find the probability of the given event.

Complete step by step solution:
Let's learn more about probability first before doing calculations.
Probability predicts how likely an event is going to occur or how likely the proposition is true. Probability of an event is always less than 1 or 1, which indicates the certainty of an event and if the probability of an event is zero it means that the impossibility of an event does exist. Higher is the probability of an event more likely an event is going to occur.
Now, we will perform the calculation part of the problem.
We have three groups and let them be named as A, B and C.
In group A we have 3 girls and 1 boy, thus total members in group A are 4.
Therefore, selection of boys will be $\dfrac{1}{4}$ and selection of girls from group A is $\dfrac{3}{4}$.
Similarly, from group B we have a selection of boys as $\dfrac{2}{4}$ and $\dfrac{2}{4}$ as girls.
From group C, selection of boy is: $\dfrac{3}{4}$ selection of girl is: $\dfrac{1}{4}$
In the question we are being stated that after selection there must be 2 boys and 1 girl;
Our selection will be likewise;
One girl from one group and two boys from the other two groups will be the combinations.
$\Rightarrow \dfrac{1}{4} \times \dfrac{1}{2} \times \dfrac{1}{4} + \dfrac{3}{4} \times \dfrac{1}{2} \times \dfrac{3}{4} + \dfrac{1}{2} \times \dfrac{1}{4} \times \dfrac{3}{4}$ (we have selected one girl and two boys alternatively from each group)
After calculations we get
$\Rightarrow \dfrac{{13}}{{32}}$

Option 3 is correct.

Note: We have a large number of applications of probability in everyday life such as, a probabilistic approach is used by Casino players, used by many insurance policy makers and in share markets probability of rise and fall of the prizes of the shares is made by the businessmen etc.