Question

There are two boys and two girls. A group of two members is to be formed. Find the probability that a group contains two boys.

Answer 1

$\large\underline{\sf{Solution-}}$

$\sf \: Committee \: of \: two \: is \: to \: be \: formed \: from \:  2 \:  boys \: and \:  girls.</p><p></p><p></p><p>[tex] \sf \: Let \: 2 \: boys \: be \: B_1, \: B_2 \: and \:  2  \: girls \: be \:  G_1,G_2.</p><p></p><p></p><p>So, Sample space is </p><p></p><p>[tex] \sf \: S \: = \{B_1B_2, \: B_1G_1, \: B_1G_2, \: B_2G_1 \: B_2G_2, \: G_1G_2 \}$

Thus,

Number of total possible outcomes is

$\bf\implies \:\:n(S) \: = \: 6$

Let E is the event that group contain 2 boys.

$\therefore \: \sf \: E \: = \{B_1B_2 \}$

Thus,

Total number of favourable outcomes are

$\bf\implies \:n(E) \: = \: 1$

Now,

we know that,

$\sf \:Probability\:of\: event =\dfrac{Number\:of \: favourable \: outcomes}{Total \: number \: of \: outcomes \: in \: sample \: space}$

Or

$\sf \: P(E) \: = \: \dfrac{n(E)}{n(S)}$

So,

$\bf\implies \:P(E) \: = \: \dfrac{1}{6}$

Explore more :-

• The sample space of a random experiment is the collection of all possible outcomes.

• An event associated with a random experiment is a subset of the sample space.

• The probability of any outcome is a number between 0 and 1.

• The probability of sure event is 1.

• The probability of impossible event is 0.

• The probabilities of all the outcomes add up to 1.

• The probability of any event A is the sum of the probabilities of the outcomes in A.