# when two dice are thrown what is the probability of getting 10 as product

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## In a throw of two dice, the probability of getting a sum of 10 is

Click here👆to get an answer to your question ✍️ In a throw of two dice, the probability of getting a sum of 10 is

Question

## In a throw of two dice, the probability of getting a sum of 10 is

**A**

12 1

**B**

36 1

**C**

6 1

**D**

4 1 Easy Open in App Solution Verified by Toppr

Correct option is A)

There are a total of 36 combinations in throw of 2 dice.

The sum of 10 could be obtained in the following cases:

5+5,4+6,6+4

That is a total of 3 cases. Therefore the required probability here is:

36 3 = 12 1

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## Two dice are thrown simultaneously. Find the probability of getting:(i) the sum as 8.(ii) a multiple of 2 on one dice and a multiple of 3 on other dice.(iii) a total of at least 10.

Two dice are thrown simultaneously. Find the probability of getting:(i) the sum as 8.(ii) a multiple of 2 on one dice and a multiple of 3 on other dice.(iii) a total of at least 10.. Ans: Hint: In this question, we are given that two dice are thrown ...

Two dice are thrown simultaneously. Find the probability of getting:(i) the sum as 8.

(ii) a multiple of 2 on one dice and a multiple of 3 on other dice.

(iii) a total of at least 10.

Answer Verified 235.5k+ views

**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

Probability=

Number of favorable outcomes

Total outcomes

Probability=Number of favorable outcomesTotal outcomes

.

**Complete step by step answer:**

Here, we are given that two dice are thrown simultaneously. As we know, a dice has 6 possibilities, therefore for two dice, the number of possibilities will be

6×6=36 6×6=36

. Let us draw sample space for the given event.

(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)

Hence, the total number of outcomes are 36.

With the help of this sample space we will find required elements for every part.

(i) Here we have to find the probability of getting the sum as 8. Therefore, let us analyze the sample space and count the numbers whose sum is 8. As we can see, following are required cases:

(2,6), (3,5), (4,4), (5,3), (6,2)

Hence, the number of favorable outcomes is 5. So,

Hence, the probability of getting the sum as 8 isProbability= 5 36 Probability=536 . 5 36 536 **.**

(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:

(2,3), (2,6), (4,3), (4,6), (6,3), (6,6), (3,2), (3,4), (3,6), (6,2), (6,4).

Hence, the number of favorable outcomes is 11. So,

Hence, probability of getting a multiple of 2 on one dice and multiple of 3 on other dice isProbability= 11 36 Probability=1136 . 11 36 1136 **.**

(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:

(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)

Hence, the number of favorable outcomes are 6. So,

Hence, the probability of getting a sum at least 10 isProbability= 6 36 = 1 6 Probability=636=16 . 1 6 16 **.**

**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.

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A box contains 20 packets of potato chips.

6 packets contain barbecue flavoured chips.

10 packets contain salt flavoured chips.

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## What is the probability of getting a sum of 10 from the numbers on the two dice?

Answer (1 of 5): There are 36 equally likely ordered pairs, like (3,4). To sum to ten, the first die must be 4 or more. So (4,6) (5,5) and (6,4) are your 3 of 36 ways to get a sum of 10. P=3/36.

What is the probability of getting a sum of 10 from the numbers on the two dice?

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Sort David Marilley

Former Financial EngineerAuthor has 2.6K answers and 1.3M answer views4y

Originally Answered: What is the probability of getting a sum of 10, the numbers on the two dice?

There are 36 equally likely ordered pairs, like (3,4). To sum to ten, the first die must be 4 or more. So (4,6) (5,5) and (6,4) are your 3 of 36 ways to get a sum of 10. P=3/36.

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Praneethreddy

Studies at Bachelor of Technology in Information Technology (Expected 2023)2y

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What is the probability of rolling a sum of 7 with two dice?

When 2 dice are rolled total possible outcomes are 36. They 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 favourable outcomes to get a sum of 7 when 2 dice are rolled simultaneously = 6

{i.e.,(1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }

Probability = favourable outcomes /total outcomes

P = 6/36 P = 1/6.

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Michael C Palau

Author has 1.5K answers and 432.9K answer viewsFeb 19

There are ways to sum to 10, 5 & 5 and 6 & 4 two ways so the odds are 1/12

odds for a number n for 1 thru 7 are n -1 & for #s 7 thru 12 are 13 - n

Michael Arthur Toft

Studied at City University London2y

There are 36 combinations of two dice.

Only 3 of those sum to 10 (5–5, 6–4, 4–6)So probability is 3/36 or 1/12

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PJ Shetty

Data analytics & hiking enthusiastic. Everest base camp 2016!!6y

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Two dice are thrown. If it is known that the sum was less than 6 the probability of getting a sum is?

For a 2 die the total combinations are 6*6 =36.

For the sum of 2 die to be less than 6, following are the combinations.

Die 1 Die 2 1 + 1 1 + 2 1 + 3 1 + 4 2 + 1 2 + 2 2 + 3 3 + 1 3 + 2 4 + 1

There are 10 combinations where the sum is less than 6. So the total probability is 10/36 =5/18

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Bruce Alan Martin

My fascination with numbers began long before I could count.Author has 1.6K answers and 5M answer views4y

Originally Answered: What is the probability of getting a sum of 10, the numbers on the two dice?

There are 36 possible outcomes for the sum of two standard (6-sided) dice, but only three of them add up to ten (6+4, 5+5, 4+6). Therefore, the probability is 3/26 = 1/12;

Stephen Zisk

Works at RedPoint Global Inc. (2016–present)Author has 996 answers and 843K answer views4y

Originally Answered: What is the probability of getting a sum of 10, the numbers on the two dice?

Let’s assume they are standard 6-sided cubic dice with 1–6 pips on their faces, and they are not fixed/loaded. If the first die shows a 4, 5, or 6, the second can show a 6, 5, or 4 respectively. So that’s three ways of making a 10 out of 36 ways of rolling the two dice (6 for the first times 6 for the second). That means the probability is 3/36 which reduces to 1/12 or 0.083. If the dice have some other shape or other sets of pips, you will get a different answer.

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Archana N

Sr Solution Lead at MResult Services Pvt. Ltd., Bangalore (2019–present)4y

Related

What is the probability of getting a product of 12 when two dice are thrown?

For two dice to multiply to 12 we have four options: (2,6),(3,4),(4,3) and (6,2)

There are 36 possibilities altogether when rolling two dice. Since there are only 4 possibilities for getting 12, this means we have 4/36 i.e. 1/9 probability of getting a product of 12 when 2 dice are thrown.

Guys, does anyone know the answer?