Probability of Rolling Doubles with Dice

The video tutorial explains how to calculate the probability of rolling doubles with two six-sided dice. It begins by defining what rolling doubles means and then explores the concept of sample space, detailing how to construct it for two dice. The tutorial further explains how to identify the outcomes that meet the criteria for rolling doubles and calculates the probability by comparing the number of successful outcomes to the total number of possible outcomes. The probability is simplified to a fraction, providing a clear understanding of the likelihood of rolling doubles.

What does it mean to roll doubles with two dice?

• The dice show consecutive numbers.

• Both dice show the same number.

• The sum of the dice is seven.

• One die shows a higher number than the other.

How many possible outcomes are there when rolling two six-sided dice?

• 48

• 24

• 36

• 12

Why are the rolls of two dice considered independent events?

• Because each die is rolled separately and does not influence the other.

• Because the outcome of one die affects the other.

• Because they are rolled at the same time.

• Because they are part of the same game.

What is a compound event in the context of rolling dice?

• An event that cannot occur.

• An event with multiple possible outcomes that satisfy it.

• An event that involves rolling more than two dice.

• An event with only one possible outcome.

How many outcomes in the sample space result in rolling doubles?

• 3

• 6

• 12

• 9

What is the probability of rolling doubles with two six-sided dice?

• 1/2

• 1/3

• 1/6

• 1/12

If the first die shows a 4, what is the probability that the second die also shows a 4?

• 1/2

• 1/3

• 1/6

• 1/1

How can the probability of rolling doubles be simplified?

• By adding the probabilities of each outcome.

• By dividing the number of favorable outcomes by the total number of outcomes.

• By multiplying the probabilities of each die.

• By subtracting the unfavorable outcomes from the total.

What fraction represents the probability of rolling doubles?

• 1/6

• 1/8

• 1/4

• 1/2

Which of the following is NOT a possible outcome when rolling two dice?

• (1, 1)

• (2, 3)

• (6, 6)

• (7, 5)