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# What is the probability of not rolling a 4 on a 6 sided die?

Some events are usually desired to happen the same as what is thought. Sometimes it might go the same way and sometimes it might not. Here we don’t have 100% confirmation for an event to happen. So, try to find out the chances of success of an event to happen and this process is termed as a probability. For example, if a card is drawn from a deck of 52 cards then it is not sure about the face on the card or the color of the card but it is desired to get a king so the chances of result in our favor is known as a probability.

### Probability

Probability is the ratio of the number of favorable outcomes to the total number of outcomes. We generally represent it by ‘p’. The favorable outcome is the subset of the total outcomes. So the number of favorable outcomes will always be less than or equal to the total number of possible outcomes. It means that the numerator of the fraction is less than the denominator. So the value of probability is less than or equal to 1. The probability of an impossible event is 0. So the probability will lie between 0 to 1.

Probability = (Number of Favorable outcomes) / (Total number of outcomes)

0 ≤ Probability (p) ≤ 1

If the probability of a happening event is ‘p’ and the non-happening of the same event is ‘q’. Then the summation of p and q will be equal to 1.

p + q = 1

q = 1 – p

So, we can conclude that the probability of non-happening of an event is (1 – p)

### What is the probability of not rolling a 4 on a 6 sided die?

Let’s learn a bit about the concept of how to solve the problem statement,

Throwing of Dice: Dice is a hard cube-type structure. It has six faces and each faces is numbered with dots from 1 to 6. When a dice is rolled then there might be the chance of getting 1, 2, 3, 4, 5, or 6. So we call them sample space. Following is the step-by-step process to solve the problem:

Step 1: Find out the sample space of the event. The rolling of dice leads to getting a value of 1, 2, 3, 4, 5, or 6.

Sample Space (S) = {1, 2, 3, 4, 5, 6}

Number of sample space, n(S) = 6

Step 2: Find out the Favorable case and then count the total number of favorable cases.

Step 3: Use the formula, Probability = (Number of the favorable events) / (Total number of possible events)

When a dice is rolled, the possibility of all occurrence events is 1, 2, 3, 4, 5, or 6.

S = {1, 2, 3, 4, 5, 6}

So the total number of possible outcomes are 6.

n(S) = 6

Favorable outcomes is not getting 4.

F = {1, 2, 3, 5, 6}

So the total number of favorable outcomes is 5.

Probability (p) =  (Number of Favorable outcomes) / (Total number of outcomes)

Probability (p) = 5/6

So the probability of the given event is 5/6.

### Similar Problems

Question 1: What is the probability of not getting an even number when a dice is rolled?

Solution:

When a dice is rolled, the possibility of all occurrence events is 1, 2, 3, 4, 5, or 6.

S = {1, 2, 3, 4, 5, 6}

So the total number of possible outcomes is 6.

n(S) = 6

Favorable outcomes are not getting even numbers.

F = {1, 3, 5}

The total number of favorable outcomes is 3.

Probability (p) =  (Number of Favorable outcomes)/(Total number of outcomes)

Probability (p) = 3/6

= 1/2

So the probability of a given statement is 1/2.

Question 2: When a dice is rolled what is the probability of getting the number multiple of 2?

Solution:

When a dice is rolled, the possibility of all occurrence events is 1, 2, 3, 4, 5, or 6.

S = {1, 2, 3, 4, 5, 6}

So the total number of possible outcomes are 6.

n(S) = 6

Favorable outcomes = numbers is not a multiple of 2.

(The number which comes in the table of 2 is known as the multiple of 2)

Favorable outcomes = {1, 3, 5}

Total numbers of favorable outcomes = 3

Probability (p) =  (Number of Favorable outcomes) / (Total number of outcomes)

Probability (p)= 3/6

= 1/2

So the probability of the given statement is 1/2.

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