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?

Question

contestada

Respuesta :

windyyork windyyork · Answer 1 · 2019-11-18T07:16:45+01:00

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

Step-by-step explanation:

Since we have given that

There are 2 dices :

1) Standard dice

2) Biased dice

Probability of getting a standard dice = [tex]\dfrac{1}{2}=0.5[/tex]

Probability of getting a biased dice = [tex]\dfrac{1}{2}=0.5[/tex]

Probability of getting 6 from standard dice = P(6|S) = [tex]\dfrac{1}{6}[/tex]

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,

[tex]P(S|6)=\dfrac{P(6|S)\times P(S)}{P(6)}=\dfrac{\dfrac{1}{6}\times 0.5}{\dfrac{1}{6}\times 0.5+1\times 0.5}=\dfrac{1}{7}[/tex]

So, the required probability would be

[tex]\dfrac{1}{7}\times \dfrac{1}{6}+1\times \dfrac{6}{7}\\\\\\\\=0.8810\\\\=88.10\%[/tex]

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