If two dice are rolled, find the probability that the sum of the die is 8. Probability that sum is 8 =
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
If two dice are rolled, find the probability that the sum of the die is 8.
Probability that sum is 8 =
(1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,1) , (2,2) , ................... , (6,5) , (6,6) are the total numbers we get when we throw a pair of dice.
That is 36.
In the question they are asking the probablity that the sum of the die is 8.
suppose dice 1's upper face gives 1.Now dice 2 can be anything between 1 and 6.But whatever might be the number on dice 2's upper face, the sum of dice 1 and dice 2 will never be 8.
Now suppose dice 1 gives 2 .Here also dice 2 can be anything between 1 and 6.But the sum of both the dices will be 8 only if the dice 2 shows 6.
Similarly now , if dice 1's face is 3 , sum will be 8 only if dice's 2 upper face shows 5.
If dice 1 shows 4 , sum will be 8 only if dice 2's upper face shows 4.
If dice 1 shows 5 , sum will be 8 only if dice 2's upper face shows 3.
If dice 1 shows 6, sum will be 8 only if dice 2's upper face shows 2.
Therefore sum will be 8 only 5 times , but the sample face consists of 36 vlues.
Therefore probablity that sum is 8 is .
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