If two identical dice are thrown simultaneously (The order of result does not matter. For example, $(2, 3)$ and $(3, 2)$ are considered same), what is the probability of getting same number on both the dice? My attempt: Though the sample space is reduced from $36$ to $21$, the probability of getting the same number on both dice is $\frac{1}{36}$, and the probability of getting different number on both the dice is $\frac{2}{36}$. Since we have $6$ possibilities of getting same number on both the dice, the required probability is $\frac{6}{36} = \frac{1}{6}$
Solution: Given, two dice are thrown at the same time. We have to find the probability of getting a different number on both dice. When 2 dice are thrown at the same time, the overall possible outcomes are (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) Total number of possible outcomes = 36 The possibility of getting different number is {(1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5)} Number of favourable outcomes = 30 Number of possible outcome = 36 Probability = number of favourable outcomes / number of possible outcomes Probability of getting different number = 30/36 = 10/12 = 5/6 Therefore, the probability of getting a different number is 5/6. ✦ Try This: Three dice are thrown at the same time. Find the probability of getting the same number on all dice. ☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14 NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 19(ii) Summary: Two dice are thrown at the same time. The probability of getting different numbers on both dice is 5/6 ☛ Related Questions: Probability is a measure of the possibility of how likely an event will occur. It is a value between 0 and 1 which shows us how favorable is the occurrence of a condition. If the probability of an event is nearer to 0, let’s say 0.2 or 0.13 then the possibility of its occurrence is less. Whereas if the probability of an event is nearer to 1, lets say 0.92 or 0.88 then it is much favourable to occur. Probability of an event The probability of an event can be defined as a number of favorable outcomes upon the total number of outcomes.
Some terms related to probability
When two dice are rolled what is the probability of getting same number on both?
Sample QuestionsQuestion 1: Find the probability of getting odd number on first dice and even number on other dice when two dice are thrown simultaneously. Answer:
Question 2: If two dice are thrown together then find the probability of getting 1 or 2 on either of the dice. Answer:
Question 3: In an event 2 dice are thrown simultaneously. Find the probability of getting prime number on first dice. Answer:
Question 4: Three coins are tossed together find the probability of getting at least one head and one tail. Answer:
Question 5: Find the probability of getting at least two tails when a coin is tossed three times. Answer:
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