what is the probability of rolling a dice at most 3 times until a 6 occurs

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what is the probability of rolling a dice at most 3 times until a 6 occurs

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Josie 3 months 2022-02-09T07:32:26+00:00 1 Answer 0 views 0

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    2022-02-09T07:34:18+00:00

    Answer:

    Probablity of getting six in at most three roll= 0.199.

    Step-by-step explanation:

    Given: Dice rolled at most 3 times untill a 6 occurs.

    First, finding the probablity of getting 6 in a dice if rolled once.

    Probablity= [tex]\frac{chances\ of\ occurance}{Total\ number\ of\ event}[/tex]

    We know, dice have six side, therefore, total number of event will be 6.

    ∴ Probablity of getting six in one roll= [tex]\frac{1}{6}[/tex]

    As given, Dice is rolled at most 3 times.

    Now, finding the probablity of getting 6 in a dice if rolled 3 times.

    ∴ Probablity of getting six in three roll= [tex]\frac{1}{6}+(\frac{1}{6})^{2} +(\frac{1}{6})^{3}[/tex]

    ⇒ Probablity of getting six in three roll=  [tex]\frac{1}{6}+\frac{1}{36} +\frac{1}{216}[/tex]

    Taking LCD 216

    ⇒Probablity of getting six in three roll= [tex]\frac{1\times 36+ 6\times 1+1}{216}[/tex]

    ⇒Probablity of getting six in three roll= [tex]\frac{43}{216}[/tex]

    Probablity of getting six in three roll=0.199

               

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