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
