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Hint: Calculate the number of possible outcomes for throwing two dice. Calculate the number of favourable outcomes for each of the cases. Use the fact that the probability of any event is the ratio of the number of favourable outcomes and the number of possible outcomes to calculate the probability of each of the events. Complete step-by-step solution - We have to calculate the probability of each of the events when two dice are thrown.We know that the total number of possible outcomes when two dice are thrown is $=6\times 6=36$.We know that the probability of any event is the ratio of the number of favourable outcomes and the number of possible outcomes.We will now calculate the probability of events in each case.(a) We have to calculate the probability that the sum of digits is a prime number.We will draw a table showing the sum of digits on rolling both the dice.
Probability defines the likelihood of occurrence of an event Answer: The probability of getting an even number on the first side when a pair of dice is thrown once is 1/2Let's look into the possible outcomes. Explanation: Sample space of a pair of dice thrown has the following possible outcomes: {(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 outcomes = 36 Let E be the event of getting an even number on the first side. Thus, favourable outcomes of event E is as follows: {(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} Total number of favourable outcomes = 18 Using the probability formula, Probability = Number of favorable outcomes / Total number of outcomes Thus, the probability of getting an even number on the first side = 18/36 = 1/2. Therefore, the probability of getting an even number on the first side when a pair of dice is thrown once is 1/2.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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