A way to visulize this is to start with asking "what situation has the least probability" on one roll of a six-sided die. The answer is any particular number, say a 1. Since there are six possible numbers, the probability is 1-in-6 or 1/6 = 0.17 (17%); now, since the total probability of any set added to the probability of the opposite outcome must be 1, then it stands that the probability of getting any of the 5 remaining numbers (2 through 6) is 1 - 0.17 = 0.83 (83%).
In fact, for any n-sided die, the probability, on one roll, of getting one of m numbers in the set of nnumbers is m/n.
Answer: if n = 6, and m = 4, because there are only 4 numbers on a six-sided die less than 5, the probability, P = 4/6 = 0.67 (67%).
Now let's extend the question and ask: what is the probability of getting a number less than 5 in each of two rolls. To answer, we must accept that each roll is a mutully exclusive set. That means the each roll has no impact whatsoeveron any other roll. Now, one could argue that this is never the case, because when the die bounces on the table, it changes the surface structure, or your hand muscles are stressed from the first roll, etc., but you would dramatically change the nature of the probability sets and make this far too technical a situation to be handled here. But in general, we say that these two die rolls have no impact on one another and are therefore mutually exclusive.
To find the probability of two mutually exclusive sets, we simply multiply the separate probabilities. Keep in mind that while the two sets are mutually exclusive, the sum of the combined probabilities, plus the opposite of the two, must be 1 (or 100%).
So, if the probability of rolling a 1,2,3, or 4 in one throw is 0.67, the doing the same in two throws is 0.67 * 0.67 = 0.44 (44%); hopefully you intuitively predicted that the probability would go down. Therefore, the probability of not throwing anything less than a 5 twice in a row is P = 1 - 0.44 = 0.56 (56%); keep in mind: this is not the probability of throwing a 5 or 6 twice in a row; it simply means not throwing a 1, 2, 3, or 4 twice in a row; for example, this could mean throwing a 1,2,3, or 4 the first time, but then throwing a 5 or 6 the second time. You have to ask "what are all the situations where it wouldn't be true?". Knowing that the probability of the opposite occurring is 56%, this should intuitively tell you that this "opposite" probability set has more possibilities.
Try this on your own: What is the probability of rolling exactly a 5, then rolling exactly a 1? Hint: what is the probability of each case on its own?
There are 6 possible numbers to roll on a die. However, there are only 4 numbers less than 5 on a die (1,2,3,4). This means 4 possibilities to roll less than a 5 divided by the total number of possibilities to roll (6). So 4/6 (the / means divided by) gives you an answer of roughly 0.667 or 2/3 or a 66.67% chance to roll a number less than 5 on a six-sided die.
There are 4 numbers less than 5, so that is 4 out of 6 or 2/3.
A total of four options; 6 options in total, all equally likely; so the probability is 4/6.
each number has 1 chance in 6 so rolling a 1 or a 2 is 1 chance in 3
The answer is 2/5. There is 1 number less than two (1) and there are 3 numbers more then 7 (8,9,10) therefore it will be 4/10 and 4/10 reduced is 2/5. -You're Welcome ;)
Any number less than 3.
The number could be anything less than 6
any negative number is less than zero
There could be many questions: What is the probability of rolling an even number. What is the probability of rolling an odd number. What is the probability of rolling a number less than 4. What is the probability of rolling a number more than 3. What is the probability of rolling 1,4, or 6. Basically it could be any question about the probability of rolling half of the faces.
The probability of rolling a number less than 1 on a standard 6-sided die is zero. It will not happen.
It is: 1 in 3
There is a 4 in 6 (or 2 in 3) probability of rolling a number less than a five on a standard number cube.
The probability is 57/216 = 19/108
It is 1.
The probability of rolling a number less than 6 on a die would be 5/6.
The probability of rolling a number on a die is 1 out of the number of sides on the die. So, for a six sided die, the probability of rolling a 4 is 1/6. The probability of rolling a 4 or a 5 becomes 2/6 or 1/3. This is because there are two acceptable outcomes out of six. So when finding the probability of rolling a number less than x on a y sided die, it becomes x-1 / y. It is x-1 because the outcome is to roll less than the number, not less than or equal.
The probability is 1.
5 over 11
It is 1/3
3 out of 6