Question

Suppose you put two dice in a bag, one of the dice has a 6 on every face. The other is a standard 6-sided die. You choose one die at random, roll it, and get a 6. If you roll the same die, what is the probability that the next roll is also a 6?

Answer 1

Answer: The probability that the next roll is also a 6 is 88.10%.

Explanation:

Since we have given that

There are 2 dices :

1) Standard dice

2) Biased dice

Probability of getting a standard dice =
`(1)/(2)=0.5`

Probability of getting a biased dice =
`(1)/(2)=0.5`

Probability of getting 6 from standard dice = P(6|S) =
`(1)/(6)`

Probability of getting 6 from biased dice = P(6|B)=1

We need to find the probability that the next roll is also a 6.

so, our probability becomes,

`P(S|6)=(P(6|S)* P(S))/(P(6))=((1)/(6)* 0.5)/((1)/(6)* 0.5+1* 0.5)=(1)/(7)`

So, the required probability would be

`(1)/(7)* (1)/(6)+1* (6)/(7)\\\\\\\\=0.8810\\\\=88.10\%`

Hence, the probability that the next roll is also a 6 is 88.10%.