When two dice are thrown, remember that the total number of oucomes is  or , NOT .  (Many students think that it is .)

Now, for the data given, we know that the following pairs will work:

Thus, there are  possible outcomes that will work for this data. This means that the probability of this outcome is  or .

To find the probability, divide the number of outcomes that fit the event description by the total possible number of outcomes. There are 31 days in January, so that is our denominator. Of those, 3,6,9,12,15,18,21,24,27,30 are divisble by three, which is 10 of the days. Thus the answer is:

The total number of outcomes that fit the event (rolling a prime number) are the number of primes below 10: 2, 3, 5, 7 for a total of 4.
divide that but the total number of outcomes (10) and reduce:

There are 2 days that begin with "t". We know those cannot be the days. Since you are guessing you can only guess 1 outcome. The chance that that day is the corect one is the number of ways you can get it right (1, by guessing it right the first time) divide by the total number of outcomes (5).

To find the probability of an event, divide the number of ways the event can happen by the total number of outcomes.

There are 11 balls that are not red, so there are 11 ways there can be a not red ball picked.

There are 14 balls total in the urn so the probability we pick a not red ball is:

Divide the total number of ways to get the desire event by the total number of outcomes.

Since it is a 20 sided die there are 20 outcomes possible, but only 6, 12, and 18 are divisible by 6.

Thus, the probability that you roll a number divisible by 6 is:

To find the probability find the total number of ways to get the described event (rolling an even number: 2,4,6,8,10 for a total of 5) divided by the total number of outcomes (10). Thus the answer is:

.

Remember to reduce the fraction!

To find the probability of an event, find the total number of ways the event can happen and divide that by the total number of outcomes. There are only  face-card diamonds (King, Queen, Jack), and there are 52 possible cards to draw. Thus:

The total number of gum drops and gummy bears is 49.  There are 7 red gum drops and gummy bears and 7 green gum drops and gummy bears.  There is a 2 in 7 probability that you will pick up a green or red gum drop or gummy bear.

If you answered 1/7, then you only accounted for choosing either red gum drop or gummy bear or green ones. 

If you answered 2/47 then you did not add the number of gum drops and gummy bears correctly.

If you answered 7 in 14 then you found the number of red or green gummy bears/gum drops out of the total red and green gummy bears and gum drops. 

And if you answered 3 out of 49, you found only the probability of choosing either red gum drops or green gummy bears. 

To find the probability of an event, find the number of ways that even can happen divided by the total number of possible outcomes.

There are 31 days in August, thus the total number of outcomes for someone being born in August is 31.

Since we only care about the event that is being born on the 17th, there is only one way that event can happen (being born on August 17th).

Thus the probability is 

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