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What is the probability of getting a 2 or a 5 when a die is rolled?

  • Difficulty Level : Medium
  • Last Updated : 22 Sep, 2021

Probability is the estimation of the possibility of random events happening, and its value ranges from 0 to 1. The probability of a sure event is always one, and the event that will never occur has a probability of zero. You may have also wondered how weather stations predict that it will rain today and how a cricket team’s winning and losing is made. Probability theory helps in finding answers to all such questions. Probability deals with the chances of occurrence of random experiments.

The probability of getting an outcome is defined as the ratio of the number of times the event is occurring to the total number of trials.  

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P(A) = (Number of times event A is occurring/Total number of Trials)



Let’s try this formula to calculate the probability of all the possible outcomes of rolling a single die. Suppose you roll a die, there are six possible outcomes. They are 1, 2, 3, 4, 5, and 6. The probability of getting 1 on die is P(1) = 1/6. Similarly, the probability of getting 2, 3, 4, 5, and 6 is also 1/6.

Terminologies Related to Probability

  • Experiment: The experiment is a trial that can be repeated infinitely, and for each trial, possible outcomes are obtained.
  • Sample space: All the possible values of trials or experiments can be represented using a Set, and this set is known as Sample space.
  • Event: The set of favorable outcomes from the performed experiment is known as an event, or one can also say that it is a subset of the sample space of the experiment.

Addition Rule of Probability

If there are two events A and B having probability as P(A) and P(B) respectively. Then, according to the addition rule of probability, the combined probability will be calculated by the formula given below.

  P(AUB) = P(A) + P(B) – P(A∩B)

What is the probability of getting a 2 or a 5 when a die is rolled?

Solution:

To find the probability of getting 2 or 5 on the face when a die is rolled. We can do this by using the formula of probability.

P(E) = (Number of times event occurs)/(Total number of trials)

Sample space of possible outcomes on rolling a die is  S = {1, 2, 3, 4, 5, 6}



If event E is the probability of getting 2 or 5 as outcome on rolling a die.  

Number of times event occurs [n(E)] = 2

Total number of trials [n(S)] = 6

P(E) = 2/6 = ⅓

Similar Questions  

Question 1: A bag has 10 balls of three colors, 4 balls of red color, 1 ball of blue color, and 5 balls of black color. If Arun picks the ball randomly. What is the probability of Arun picking up a red color ball from the bag?

Solution:

Number of Red Balls = 4

Number of Blue Balls = 1

Number of Black Balls = 5

Total number of balls = 10

P(E) = (Number of times event occurs)/(Total number of trials)

∴ P(Red Ball) = (4/10) = 2/5 = 0.40

Question 2: A weather forecasting station predicts the probability of rain as 0.54. Then what is the probability of prediction to be incorrect?

Solution:

P(Raining) = 0.54

P(Rain data to be false) = ?

P(Event to occur) + P(Event will not occur) = 1

∴ P(Rain data to be false) = 1 – P(Raining) = 1 – 0.54 = 0.46

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