what is the probability of rolling a dice at most 3 times until a 6 occurs Question what is the probability of rolling a dice at most 3 times until a 6 occurs in progress 0 Math Josie 3 months 2022-02-09T07:32:26+00:00 2022-02-09T07:32:26+00:00 1 Answer 0 views 0

## Answers ( )

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