What is the probability of getting a 5 If a die is tossed once?

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What is the probability of getting a 6 when a die is thrown once?
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A die is thrown twice. What is the probability that (i) 5 will not come up either time? (ii) 5 will come up at least once? [Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]

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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.

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 6 when a die is thrown once?

Solution:

To find the probability of getting 6 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 6 as the outcome on rolling a die.

Number of times event occurs [n(E)] = 1
Total number of trials [n(S)] = 6
P(E) = 1/6 = 0.167

Similar Questions

Question 1: What is the probability of getting 5 when a die is thrown?

Solution:

To find the probability of getting 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 5 as the outcome on rolling a die.
Number of times event occurs [n(E)] = 1
Total number of trials [n(S)] = 6
P(E) = 1/6 = 0.167

Question 2: What is the probability of getting 2 when a die is thrown?

Solution:

To find the probability of getting 2 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 as the outcome on rolling a die.
Number of times event occurs [n(E)] = 1
Total number of trials [n(S)] = 6
P(E) = 1/6 = 0.167

Question 3: What is the probability of getting 6 or 3 when a die is thrown?

Solution:

To find the probability of getting 6 or 3 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 6 or 2 as the outcome on rolling a die.
Number of times event occurs [n(E)] = 2
Total number of trials [n(S)] = 6
P(E) = 2/6 = 1/3 = 0.333…

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Which of the following arguments are correct and which are not correct ? Give reasons for your answer.

If a die is thrown once, the possible outcomes areS = {1, 2, 3, 4,5, 6} i.e. n(S) = 6Let A be the favourable outcomes of getting add number. ThenA = {1,3,5} i.e. n(S) = 3

Therefore, P(A) =

Thus, the given statement is correct.

Solution:

Total number of outcomes when die is thrown twice = 6 × 6 = 36.

(i) Number of possible outcomes when 5 will come up either time = (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5) = 11

Probability that 5 will come up either time = Number of possible outcomes/Total number of favourable outcomes

= 11/36

The probability that 5 will not come up either time = 1 - 11/36

= 25/36

(ii) Number of possible outcomes when 5 will come up at least once = 11

The probability that 5 comes up at least once = Number of possible outcomes/Total number of favourable outcomes

= 11/36

The probability that 5 will not come up either time is 25/36 and the probability that 5 will come up is 11/36.

Check out more about terms of probability.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 15

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