Question

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

Answer 1

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

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=
`(chances\ of\ occurance)/(Total\ number\ of\ event)`

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

∴ Probablity of getting six in one roll=
`(1)/(6)`

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=
`(1)/(6)+((1)/(6))^(2) +((1)/(6))^(3)`

⇒ Probablity of getting six in three roll=
`(1)/(6)+(1)/(36) +(1)/(216)`

Taking LCD 216

⇒Probablity of getting six in three roll=
`(1* 36+ 6* 1+1)/(216)`

⇒Probablity of getting six in three roll=
`(43)/(216)`

∴Probablity of getting six in three roll=0.199