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

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