Mathematics

Question

Annie and her friends start a Doubles Club. The numbers below show information about all the members of the club. Boys Girls Juniors 6 8 Seniors 16 12 Express the probability that Annie chooses a girl or a junior. Use the formula: P(AUB)= P(A)+P(B)- P(AnB)

2 Answer

  • 20/42 + 14/42 - 8/42 = 26/42
  • Answer: [tex]\dfrac{13}{21}[/tex]

    Step-by-step explanation:

    The given table :

                     Boys         Girls

    Juniors       6               8

    Seniors      16              12

    Let G denote the event of choosing girl and J denote the event of choosing Junior.

    Number of girls : 8+12=20

    Number of Juniors : 6+8=14

    Members that are girl and junior = 8

    Total students : 6+8+16+12=42

    The probability of choosing girl is given by :-

    [tex]P(G)=\dfrac{20}{42}[/tex]

    The probability of choosing junior is given by :-

    [tex]P(J)=\dfrac{14}{42}[/tex]

    The probability of choosing a girl and junior is given by ;-

    [tex]P(G\cap J)=\dfrac{8}{42}[/tex]

    Now, the probability choosing a girl or a junior is given by :-

    [tex]P(G\cup J)=P(G)+P(J)-P(G\cap J)\\\\=\dfrac{20}{42}+\dfrac{14}{42}-\dfrac{8}{42}\\\\=\dfrac{26}{42}=\dfrac{13}{21}[/tex]

    Hence, the  probability that Annie chooses a girl or a junior= [tex]\dfrac{13}{21}[/tex]

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