Question 70945: a die is rolled. the sample space of equally likely outcomes is {1,2,3,4,5,6} find the probability of getting a 6. Thanks =)
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The sample space tells you that there are 6 equally likely outcomes possible. Of those
6 outcomes, you are looking for only one of them ... the 6. So you have 1 chance in 6 of
getting a 6. Therefore, the probability of getting a 6 is 1 in 6, or  , or 0.166666...,
or by converting the decimal form to percent you have a 16.6666... percent probability
of getting an outcome of 6 on each roll of the die.
.
Another way of thinking about it is that with equally likely outcomes, if you roll a die
six times you would expect that on one of those rolls you would get a 1, on another
roll you would get a 2, on another roll you would get a 3, on another roll you would
get a 4, on another roll you would get a 5, and on another roll you would get a 6. (Note
that the numbers do not necessarily appear in order. You might get a 5 on the first roll,
a 1 on the second roll and so on, but after 6 rolls you should have received each number
one time.) Therefore, in the 6 rolls you have 1 successful outcome of the number 6. Getting
one 6 as an outcome in 6 rolls is transferred to probability by dividing the number of
trials (6 rolls) into the number of successful outcomes (you got a 6 one time) which again
is 1 divided by 6 for the probability.
.
In real life things don't work that way, of course. But in a very large number
of rolls you could reasonably expect that on of them you would get a 1, on
another of the rolls you would get a 2, and so on.
.
Hopefully this makes a little sense to you.
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