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Gmat quant topic 8 probability solutions
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### one dice red and one green, both fair, are rolled. Wich is the prob.pdf

1. one dice red and one green, both fair, are rolled. Wich is the probability that the sum is 5, given that the dice have opposite parity Solution okay so since dice only are numbered 1-6 and the dice have opposite parity (meaning one die will be showing and even # and the other will show an odd number), the choices you have are red- 1, 3, 5 green- 2, 4, 6 since it is 3 #s for red and 3 for green, you multiply 3x3 to figure out the possible # of outcomes (ex. 1 and 2, 1 and 4, 1 and 6, 3 and 2, 3 and 4, 3 and 6, ect.) So, 3X3=9 Then, you determine out of the 9 outcomes, how many have a sum of 5? 1 + 2= 3 NO 1 + 4= 5 YES 1 + 6= 7 NO 3 + 2= 5 YES 3 + 4= 7 NO 3 + 6= 9 NO 5 + 2= 7 NO 5 + 4= 9 NO 5 + 6= 11 NO out of the 9 outcomes, only 2 of them have a sum of 5 (1 and 4 & 3 and 2) therefore, the probability of the sum being 5 is 7/9, or 78%
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