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    Subject

    Quantitative Aptitude

    Topic

    Probability

    Tickets are numbered from 1 to 18 are mixed up together and then 9 tickets are drawn at random. Find the probability that the ticket has a number, which is a multiple of 2 or 3.

    ক)
    1/3
    খ)
    3/5
    গ)
    2/3
    ঘ)
    5/6

    Explanation

    S = { 1, 2, 3, 4, .....18 } => n(S) = 18 E1 = {2, 4, 6, 8, 10, 12, 14, 16, 18} => n(E1) = 9 E2 = {3, 6, 9, 12, 15, 18 } => n(E2) = 6 E3  =(E1∩E2)={6,  12,  18}E3\;=\left(E1\cap E2\right)=\{6,\;12,\;18\} => n(E3) = 3 ∴E=E1  ∪  E2  =  E1+E2−E3\therefore E=E1\;\cup\;E2\;=\;E1+E2-E3 => n(E) = 9 + 6 - 3 =12 where E = { 2, 3, 4, 6, 8, 9, 10, 12, 12, 14, 15, 16, 18 } ∴P(E)=n(E)n(S)=1218=23\therefore P(E)=\frac{n(E)}{n(S)}=\frac{12}{18}=\frac23

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