If two dice are thrown together then the probability of getting a sum of 13 on both dice
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Hint: In this question, we are given that two dice are thrown simultaneously and we have to find various probabilities of numbers shown on both dice. For this, we will first make sample space and then use that to find favorable outcomes for finding each probability. Total outcomes will be given as the number of elements in sample space. Probability of any event is given as $\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}$. Complete step by
step answer: Hence, the probability of getting the sum as 8 is $\dfrac{5}{36}$. (ii) Let us analyze the sample space and count numbers whose one number is multiple of 2 i.e. 2, 4, 6 and another number is multiple of 3 i.e. 3, 6. As we can see, following are required cases: Hence, probability of getting a multiple of 2 on one dice and multiple of 3 on other dice is $\dfrac{11}{36}$. (iii) Now, let us count numbers whose sum is at least 10, therefore, we have to count numbers whose sum is 10, 11 or 12. As we can see, following are the required cases: Hence, the probability of getting a sum at least 10 is $\dfrac{1}{6}$. Note: Students should carefully count all the possibilities while calculating probability. In (ii) part, students should note that multiple of 2 or 3 can be on any of the two dices. For example, (2,3) and (3,2) both are favorable cases. In (iii) part, students should note that sum should be at least 10, so, they have to consider sum as 10 or higher. Try to avoid mistakes while making sample space. 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:
What is the probability that the sum of two dice is 13?The highest sum possible when rolling a pair of dice is 12(getting 6 on both dies). So getting a sum of 13 is an impossible event. Hence, the probability is 0.
What are the probability that sum of outcomes is 13 when three dice?Probability of a sum of 13: 21/216 = 9.7%
When two dice are rolled find the probability of getting a sum less than 13?∴ Probability of getting sum equal to less than 13 is = 36/36 = 1.
What is the probability of rolling a sum of 14 with two dice?What is the probability of getting a sum of 14 when two dice are thrown simultaneously? So, pairs with sum 14 are 0.
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