A man had three dice in his pocket: one is a fair die; one is a die with threes on all sides; and one is a die with two threes, two fours and one five and one six. The man selects one of those dice with probability 1/3, 1/6 and 1/2 respectively, and then rolls that die. Use law of total probability to determine the probability of rolling a three
Answers
Answer:
Probability Rules:
The probability of two or more continuous events happening one after another is determined by the multiplication rule where the individual probability is multiplied to give the required probability. The probability that any one of the given numbers of events would happen is given by the addition rule where the addition of the individual probabilities of the events gives the required probability.
Given: A man had three dice in his pocket: one is a fair die; one is a die with threes on all sides; and one is a die with two threes, two fours and one five and one six.
The man selects one of those dice with probability 1/3, 1/6 and 1/2 respectively, and then rolls that die.
To Find: The probability of rolling a three
Solution:
Probability of picking fair dice = 1/3
Probability of Getting 3 on fair dice = 1/6
Probability of picking fair dice and getting 3 = (1/3)(1/6) = 1/18
Probability of picking a dice with threes on all sides = 1/6
Probability of Getting 3 on a dice with threes on all sides= 6/6 = 1
Probability of picking a dice with threes on all sides and getting 3 = (1/6)(1) = 1/6
Probability of picking last dice = 1/2
Probability of Getting 3 on last dice = 2/6 = 1/3
Probability of picking last dice and getting 3 = (1/2)(1/3) = 1/6
Probability of Getting 3 = 1/18 + 1/6 + 1/6
= (1 + 3 + 3)/18
= 7/18
probability of rolling a three = 7/18
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