## What is the expected sum of the numbers appear when three fair dice are rolled?

E(S) = E(s1+s2+s3) = E(s1)+E(s2)+E(s3). The expectation of the sum is the sum of the expectation values for the three dice. But since they are all fair dice they have the same expectation values. Hence **E(S) = 3 E(s1)**.

## What is the expected value of the sum of three dice?

Rolling three dice would give you an expected outcome of **10.5**. (It may be interesting to note that the expected value is an impossible occurrence since dice have a whole number of dots.

## When 3 dice are rolled what is the probability of getting a sum of 16?

Probability of a sum of 16: 6/216 = **2.8%**

## What is the most likely total when rolling three dice?

The most likely roll with three dice is a **10 or 11** both of which have the same probability: [(9 2)-3-6] /63 = 27/216 = 1/8.

## What is the probability of getting a sum of 3 If a dice is thrown?

Total | Number of combinations | Probability |
---|---|---|

2 | 1 | 2.78% |

3 | 2 |
5.56% |

4 | 3 | 8.33% |

5 | 4 | 11.11% |

## What is the expected value of the sum of the numbers that appear when a pair of fair dice is rolled?

The expectation of the sum of two (independent) dice is the sum of expectations of each die which is **3.5 + 3.5 = 7**. Similarly for N dice throws the expectation of the sum should be N * 3.5. If you’re taking only the maximum value of the two dice throws then your answer 4.47 is correct.

## What is the probability of 3 dice?

Roll a… | Probability |
---|---|

3 | 3/36 (8.333%) |

4 | 6/36 (16.667%) |

5 | 10/36 (27.778%) |

6 | 15/36 (41.667%) |

## How many possibilities are there with 4 dice?

My initial reaction is to say that the answer is 64 since 4 dice can have **6 outcomes**.

## What is the probability of getting a sum of 9 when rolling two dice?

**1/9**.

## When 3 dice are rolled what is the probability of getting a sum of 8?

1. You roll 2 dice. What is the probability that the sum is 7 if at least one of the two numbers is a 5? There are 2 ways to roll a 7 if at least one number is a 5 and there are 11 ways to roll at least one 5 so the probability is **2/11**.

## What is the probability of getting a sum of 13 when rolling a pair of dice?

Right Answer is: A

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 .

## What is the probability of rolling a sum of 4?

**1/12**.

## When three dice are rolled what is the probability that all the three dice show the same number?

So assuming the dice are ‘fair’ (that each of the six numbers has a probability of 1/6 of showing up on each of the dice) there is a probability of **1/36** that all three dice will show the same number.

## What is the probability that the sum of the numbers on your dice is at most 7?

For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is **6/36 = 1/6**.

## What is the probability that the sum of the numbers on your dice is at most 6?

**5/36**.

## What is the probability of getting 53 Mondays in a leap year?

In a leap year there will be 52 Mondays and 2 days will be left. Of these total 7 outcomes the favourable outcomes are 2. Hence the probability of getting 53 Mondays in a leap year P(E) = **2/7**.

## What is the probability that a prime number selected at random from numbers 1 2 3 35?

Hence the required probability of getting a prime number P(E1) = **11/35** .

## What is the probability that an ordinary year has 53 Sundays?

1 / 7

In 365 days Number of weeks = 52 weeks and 1 day is remaining. 1 remaining day can be Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday. Total of 7 outcomes the favourable outcome is 1. ∴ probability of getting 53 Sundays = 1 / 7.

## How do you find the expected sum?

The expected value of the sum of several random variables is equal to the sum of their expectations e.g. **E[X+Y] = E[X]+ E[Y]** . On the other hand the expected value of the product of two random variables is not necessarily the product of the expected values.

## What is the expected value of the max of two dice ? Rolls pick closest answer?

Interview Answers

Therefore the expected value of the max is (1 + 2*3 + 3*5 + 4*7 + 5*9 + 6*11) / 36 = **161/36**.

## How do you find the expected value of dice rolls?

The expected value of the random variable is (in some sense) its average value. You compute it by **multiplying each value x of the random variable by the probability P(X=x)** and then adding up the results. So the average sum of dice is: E(X) = 2 ^{.} 1/36 + 3 ^{.} 2/36 + ….

## How do you solve dice problems?

## What is the probability that all three dice show different numbers?

**5/9**.

## What is the probability of rolling triples with three dice?

Now what is the total number of outcomes? 6x6x6 = 216. Therefore the probability of a triple is **6/216 = 1/36**.

## How many possibilities are there with 2 dice?

**36 different and unique ways**the dice can come up. This figure is arrived at by multiplying the number of ways the first die can come up (six) by the number of ways the second die can come up (six). 6 x 6 = 36.

## How many combinations of 5 dice are there?

The last die may have six values. For each of these six values the second- to-last die may have six values. Thus we have 6·6 = 36 possible outcomes for the last two dice. By extension we have a total of **65 = 7776 possible outcomes** for all five dice.

## How many dices are possible?

Note that there are **36 possibilities** for (a b). This total number of possibilities can be obtained from the multiplication principle: there are 6 possibilities for a and for each outcome for a there are 6 possibilities for b. So the total number of joint outcomes (a b) is 6 times 6 which is 36.

## What is the probability that the sum is 9?

The probability of getting 9 as the sum when 2 dice are thrown is **1/9**.

## Is it more likely to obtain a sum of 9 when rolling two fair dice or when rolling three?

Which is more likely rolling a total of 9 when two dice are rolled or rolling a total of 9 when three dice are rolled? Answer: 9 = 3+6 = 4+5 = 5+4 = 6+3 — 4 ways to get total of 9 points rolling two dice so the probability that the outcome is 9 points is: 4/(6*6) = 1/9 = **0.111**.

## How many outcomes have a sum of at least 9?

(ii) two numbers appearing on them whose sum is 9. Therefore total number of possible outcomes = **36**.

## What is the probability of rolling a dice 3 times and getting a different number each time?

Thus the actual probability of getting three different numbers **is** 56⋅23=59.

## What is the probability of getting a sum of 15 if 3 dice are thrown simultaneously?

**5/108**.

## When three dice are rolled the numbers of elementary events are?

When three dices are thrown together the total number of elementary events associated is 6^{3} = ( 6 × 6 × 6) = **216**.

## What is the probability of the sum of 13?

## Die rolling probability | Probability and combinatorics | Precalculus | Khan Academy

## Probability – P(11) When Two Dice are Rolled? | Don’t Memorise

## Probability Distribution – Sum of Two Dice

## 13 Let X denote the sum of the numbers obtained when two fair dice are rolled Find the variance an