Four dice are rolled. P(a die shows 2 when one die is thrown) = 1/6. P(a die does not show 2 ie., shows 1, 3,4,5 or 6) = 5/6. Throwing of each die a fair and independent event.

## When four dice are rolled simultaneously in how many outcomes will at least one of the dice shows 3?

When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3? Explanation: When 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6 = **1296** outcomes. The number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5 = 625 outcomes.

## What is the probability that at least one of the dice is a 4?

Originally Answered: What is the probability of getting at least one 4 when you throw 2 dices? Getting 4 in one is 1/6 and in second is again 1/6. Probability of getting 4 in both is **1/36**.

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

Probabilities for the two dice

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

4 | 3 | 8.33% |

5 | 4 | 11.11% |

6 | 5 | 13.89% |

7 | 6 |
16.67% |

## How many ways are there to roll at least one 6?

So counting them, we get 11 of the possible **36 outcomes** of which at least one 6 is rolled. Now simply express this probability as a fraction! P(X=1) = P(the first dice has 6, the second hasn’t) + P(the second dice has 6, the first one hasn’t) = 1/6 * 5/6 + 5/6 * 1/6 = 5/ 36 + 5/36 = 5/18 = 0.2778.

## How many ways can 4 dice be rolled?

When 4 dice are rolled simultaneously, there will be a total of 6^4=**1296 outcomes**.

## When 4 dice are thrown what is the probability?

Probability=4/1296=**1/324**.

## What is the probability of getting at least one 6?

a) Consider the complement problem, there is a 5/6 probability of not rolling a six for any given die, and since the four dice are independent, the probability of not rolling a six is (5/6)4 = 54/64 = 625/1296. The probability of rolling at least one six is therefore **1 − 625/1296 = 671/1296 ≈** .

## What is the probability of getting at least one six?

Question: What is the probability of getting at least one six in a single throw of three unbiased dice? Answer: The probability of getting either 1 or 2 or 3 or 4 or 5 when one dice is thrown is 5/6 x 5/6 x 5/6 for 3 dices = **125/216**. This is the probability of getting at lease one 6 when 3 dices are thrown.