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All you math geniuses
#6
The question is asking what the odds are that one or  the other would happen. 2/3 is on the right track, but you forgot a step.

In fact, 2/3 would be the correct answer if the question was changed from:

Quote:The faces of a fair cube are numbered 1 through 6; the probability of rolling any number from 1 through 6 is equally likely. If the cube is rolled twice, what is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll?

to

Quote:The faces of a fair cube are numbered 1 through 6; the probability of rolling any number from 1 through 6 is equally likely. If the cube is rolled twice, what is the probability that an even number will appear on the top face in the first roll, that the number 1 will appear on the top face in the second roll, or that both would occur simultaneously?

The word "or" means that we actually need to exclude the option of both happening.


If the probability of rolling an even face on the first roll is R1 and the probability of rolling a 1 on the second roll is R2, then we can calculate the likelihood for each.

R1 = Number of even faces / number of total faces = 3/6
R2 = Number of faces with a value of 1 / number of total faces = 1/6

The probability of the independent occurrence of either OR both events, removing constraints, is simply Rn = R1+R2+R3...
Or: 2/3

The intersection of probabilities can be calculated using Rn = R1*R2*R3...
Thus: R1*R2 = R3, R1 * R2 = 3/36 = 1/12
R3 = 1/12

To find the union of probabilities, you take the probability of independent occurrence minus the intersection of probabilities, or 2/3 - 1/12 = 8/12 - 1/12 = 7/12
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Messages In This Thread
All you math geniuses - by categ - 11-15-2009, 09:56 AM
RE: All you math geniuses - by will1030 - 11-30-2019, 02:56 PM
RE: All you math geniuses - by Thorne - 09-27-2020, 01:40 PM
All you math geniuses - by Bob - 11-15-2009, 10:15 AM
All you math geniuses - by categ - 11-15-2009, 10:55 AM
All you math geniuses - by Bob - 11-15-2009, 11:14 AM

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