Question

There are three boys and two girls. A committee of two is to be formed. Find the probability of the following events:
Event A: The committee contains at least one boy.
Event B: The committee contains one boy and one girl.

Answer 1

Probability is the prediction or we can say that the probability is the prediction of the occurrence of an event .
Probability is defined as the ratio of the favorable events to the total number of events.
$P\left( N \right) \Rightarrow \dfrac{{\text favorable\ event}}{{total\ events}}$(Probability of event N)
Using this definition of probability we will find the probability of the two events given in the question.

Complete step-by-step answer:
Let us discuss probability in much more detail to do the calculation work.
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 come to the calculation part of the problem.
For Event A:
We have three boys and two girls.$(B_1, B_2, B_3, G_1, G_2)$
Total number of groups:${B_1B_2, B_2B_3, B_1B_3, B_1G_1, B_1G2, B_2G_1, B_2G_2, B_3G_1, B_3G_2, G_1G_2}$
Let us denote Boy with B and girl with G.
Condition of event A says that at least a boy must be there in the committee.
Grouping is done as: B1B2 ,B2B3, B1B3 ,B1G1, B1G2, B2G1, B2G2, B3G1, B3G2
Therefore probability of Event A is given as;
$P\left( A \right) \Rightarrow \dfrac{{\text favorable\ event}}{{total\ events}}$
Favorable event are nine and total is 10;
$\Rightarrow \dfrac{9}{{10}}$ (It is the probability of the Event A)
Similarly for event B;
Grouping is done with one boy and one girl:
${ B_1G_1, B_1G_2, B_2G_1, B_2G_2, B_3G_1, B_3G_2}$
Probability of event B is;
$P\left( B \right) = \dfrac{{\text favorable\ event}}{{total\ events}}$
$\Rightarrow \dfrac{6}{{10}}or\dfrac{3}{5}$ (probability of event B)

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.