Question

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

Answer 1

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= $\frac{chances\ of\ occurance}{Total\ number\ of\ event}$

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

∴ Probablity of getting six in one roll= $\frac{1}{6}$

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= $\frac{1}{6}+(\frac{1}{6})^{2} +(\frac{1}{6})^{3}$

⇒ Probablity of getting six in three roll=  $\frac{1}{6}+\frac{1}{36} +\frac{1}{216}$

Taking LCD 216

⇒Probablity of getting six in three roll= $\frac{1\times 36+ 6\times 1+1}{216}$

⇒Probablity of getting six in three roll= $\frac{43}{216}$

∴Probablity of getting six in three roll=0.199