A specially made pair of dice has only one- and two-spots on the faces. One of t

Question

A specially made pair of dice has only one- and two-spots on the faces. One of the dice has three faces with a one-spot and three faces with a two-spot. The other die has two faces with a one-spot and four faces with a two-spot. One of the dice is selected at random and then rolled six times. If a two-spot shows up twice, what is the probability that it is the die with the four two-spots?

The probability that it is the die with the four two-spots is _______

(Simplify your answer. Do not round until the final answer. Then round to four decimal places as needed.)

Explanation / Answer

One die is 1 1 1 2 2 2
The other is 1 1 2 2 2 2

If we roll the first one 6 times,
chances of 2 two and 4 * 1/2^6 = 3/32

If you roll the second one 6 times,
chances of 2 two and 4 * (2/3)^2 * (1/3)^4 = 8/243

So the probability it was the second die is
(8/243) / (8/243 + 3/32) = 256/958= 0.2599

So the probability it was the second die is = .2599

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