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Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.
Asked by Dr. Last Modified
Answer 
Vishaka Bhutia
Home Tutor
When dice is thrown, number of observations in the sample space = 6 × 6 = 36
Let A be the event that the sum of the numbers on the dice is 4 and B be the event that the two numbers appearing on throwing the two dice are different.
∴ A = {(1, 3), (2, 2), (3, 1)}
B=?????????????????????(1, 2)(2, 1)(3, 1)(4, 1)(5, 1)(6, 1)(1, 3)(2, 3)(3, 2)(4, 2)(5, 2)(6, 2)(1, 4)(2, 4)(3, 4)(4, 3)(5, 3)(6, 3)(1, 5)(2, 5)(3, 5)(4, 5)(5, 4)(6, 4)(1, 6)(2, 6)(3, 6)(4, 6)(5,6)(6, 5)?????????????????????B=1, 21, 31, 41, 51, 62, 12, 32, 42, 52, 63, 13, 23, 43, 53, 64, 14, 24, 34, 54, 65, 15, 25, 35, 45,66, 16, 26, 36, 46, 5
A∩B = {(1, 3), (3, 1)}A∩B = 1, 3, 3, 1
∴ P(B) = 3036=563036=56 and P(A∩B) = 236=118PA∩B = 236=118
Let P (A|B) represent the probability that the sum of the numbers on the dice is 4, given that the two numbers appearing on throwing the two dice are different.
Therefore, the required probability is 
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