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What is the probability to get a 6 three times in a row when rolling a dice?

  • Last Updated : 26 Oct, 2021

Probability is a part of mathematics that deals with the possibility of happening events. It is to forecast that what are the possible chances that the events will occur or the event will not occur. The probability as a number lies between 0 and 1 only and can also be written in the form of a percentage or fraction. The probability of likely event B is often written as P(B). Here P shows the possibility and B show the happening of an event. Similarly, the probability of any event is often written as P(). When the end outcome of an event is not confirmed we use the probabilities of certain outcomes—how likely they occur or what are the chances of their occurring.

Though probability started with a gamble, in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc., it has been used carefully.

To understand probability more accurately we take an example as rolling a dice:

The possible outcomes are — 1, 2, 3, 4, 5, and 6.

The probability of getting any of the outcomes is 1/6. As the possibility of happening of an event is an equally likely event so there is the same chance of getting any number in this case it is either 1/6 or 50/3%.

Formula of Probability

Probability of an event = {Number of ways it can occur} ⁄ {Total number of outcomes}

P(A) = {Number of ways A occurs} ⁄ {Total number of outcomes}

Types of Events

  • Equally Likely Events: After rolling a dice the probability of getting any of the likely events is 1/6. As the event is an equally likely event so there is same possibility of getting any number in this case it is either 1/6 in fair dice rolling.
  • Complementary Events: There is a possibility of only two outcomes which is an event will occur or not. Like a person will play or not play, buying a laptop or not buying a laptop, etc. are examples of complementary events.

What is the probability to get a 6 three times in a row when rolling a dice?

Solution:-

Probability of an event = (number of favourable event) / (total number of event).

P(B) = (Event B) / (total number of event).

Probability of getting 6 = 1/6.

Rolling of an dice is an independent event, it is not dependent on how many times it’s been rolled.



Probability of getting 6 three times in a row = probability of getting 6 first time × probability of getting 6 second time × probability of getting 6 third time.

Probability of getting 6 three times in a row  = (1/6) × (1/6) × (1/6) = 1/216.

Hence, the probability of getting 6 three times in a row is 0.463%.

Similar Questions

Question 1: What is the probability of rolling a 5 on a dice 3 times?

Solution:

Probability of an event = (number of favourable event) / (total number of event).

P(B) = (Event B) / (total number of event).

Probability of getting 5 = 1/6.

Rolling of an dice is an independent event, it is not dependent on how many times it’s been rolled.

Probability of getting 5 three times in a row = probability of getting 5 first time × probability of getting 5 second time × probability of getting 5 third time.



Probability of getting 5 three times in a row  = (1/6) × (1/6) × (1/6) = 1/216.

Hence, the probability of getting 5 three times in a row is 0.463%.

Question 2. What is the chance of rolling a 1 two times in a row?

Solution:

Probability of an event = (number of favourable event) / (total number of event).

P(B) = (Event B) / (total number of event).

Probability of getting 1 = 1/6.

Rolling of an dice is an independent event, it is not dependent on how many times it’s been rolled.

Probability of getting 1 two times in a row = probability of getting 1 first time × probability of getting 1 second time.

Probability of getting 1 two times in a row = (1/6) × (1/6) = 1/36.

Hence, the probability of getting 1 two times in a row 2.77 %.

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