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.

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1. [tex]\large\underline{\sf{Solution-}}[/tex]

   [tex] \sf \: Committee \: of \: two \: is \: to \: be \: formed \: from \: 2 \: boys \: and \: girls.

   [tex] \sf \: Let \: 2 \: boys \: be \: B_1, \: B_2 \: and \: 2 \: girls \: be \: G_1,G_2.

   So, Sample space is

   [tex] \sf \: S \: = \{B_1B_2, \: B_1G_1, \: B_1G_2, \: B_2G_1 \: B_2G_2, \: G_1G_2 \}[/tex]

   Thus,

   Number of total possible outcomes is

   [tex]\bf\implies \:\:n(S) \: = \: 6[/tex]

   Let E is the event that group contain 2 boys.

   [tex] \therefore \: \sf \: E \: = \{B_1B_2 \}[/tex]

   Thus,

   Total number of favourable outcomes are

   [tex]\bf\implies \:n(E) \: = \: 1[/tex]

   Now,

   we know that,

   [tex]\sf \:Probability\:of\: event =\dfrac{Number\:of \: favourable \: outcomes}{Total \: number \: of \: outcomes \: in \: sample \: space}[/tex]

   Or

   [tex] \sf \: P(E) \: = \: \dfrac{n(E)}{n(S)} [/tex]

   So,

   [tex]\bf\implies \:P(E) \: = \: \dfrac{1}{6} [/tex]

   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.

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