We have two dice. One is fair and the other is biased. The biased die is weighted to land on every of rolls. There is an equal probability for all of the other five faces on the biased die. Without knowing which one we are choosing, we pick one of the dice, roll it, and get a . What is the probability that we roll the fair die?
Answers
Given : two dice.
One is fair and the other is biased.
The biased die is weighted to land on 6 every 1 of 36 rolls.
There is an equal probability for all of the other five faces on the biased die.
Without knowing which one we are choosing, we pick one of the dice, roll it, and get a 6.
To Find : What is the probability that we roll the fair die
Solution:
Probability of getting 6 = P(6) on biased + P(6) on fair
= (1/2) (1/36) + (1/2)(1/6)
= (1/2) ( 7/36)
probability that we roll the fair die = P(6) on fair / P(6) in Total
= (1/2) (1/6) / ( 1/2) (7/36)
= (1/6)/ (7/36)
= 36 / (6 * 7)
= 6/7
probability that we roll the fair die = 6/7
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