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

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.

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.  

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.

• 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.

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)

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

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

Related Articles:

• Dependent and Independent Events
• Probability Formulas
• Bayes’ Theorem
• Tossing a Coin Probability Formula
• Types of Events in Probability

What is the definition of probability?

Probability is a measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).

How many sides does a standard die have?

A standard die has six sides.

What is the probability of rolling an even number on a fair six-sided die?

There are three even numbers (2, 4, and 6) out of six possible outcomes, so the probability is 3/6 = 1/2​.

If two fair six-sided dice are rolled, what is the probability of getting a sum of 7?

The possible combinations that result in a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), which is six out of 36 possible outcomes. So, the probability is 6/36 = 1/6​.

What is the probability of rolling a number greater than 4 on a standard six-sided die?

There are two numbers greater than 4 (5 and 6) out of six possible outcomes, so the probability is 2/6 = 1/3​.