SOLUTION:

Question 83384:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
A single die is rolled. What is the probability of rolling the following:
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(a) P(4)
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A single die has 6 numbers on it ... 1, 2, 3, 4, 5, and 6. Since only one of these
numbers is 4 and since all six numbers are equally likely to come up, there is one chance
in 6 that the number will be a 4. So the answer is . Think of it this way:
in six rolls of the die you should see each of the 6 likely numbers, one of which will
be a 4. So it is 1 chance out of 6 rolls, not 1 out of 5.
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(b) P(a number greater than 4)
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On the die there are two numbers greater than 4. (The numbers are 5 and 6). Therefore,
of the six numbers that can come up, two of them are greater than 4. So the probability
of a number greater than 4 is or 2 out of 6 which is a fraction
that simplifies
to . The answer is .
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You identified the 2 correctly, but you needed to put it over 6, not over 4. On six
rolls of the die you can get all six numbers, two of which will be the 5 and the 6. So
the probability is 2 out of 6 rolls which reduces to
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(c) P(a number greater than 6)
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There is no number on the die that is greater than 6. Therefore, you could roll the die
forever and you would never see a number greater than 6. The probability of getting
a number greater than 6 is zero. (Your answer of 0/6 is OK, but it reduces to just zero.)
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(d) P(a number less than 7)
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Every number on the die is less than seven. Therefore, every roll of the die will produce
a number less than seven. You are correct that is the probability of this
happening, but simplifies to 1. So the probability is 1 or 100%.
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Hope this helps you understand probability a little better.