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Probability of Rolling Dice

Grade 7 Math Worksheets

When rolling a standard six-sided die, the probability of rolling any given number is 1/6. This is because there are six equally likely outcomes, and each outcome has a probability of 1/6.

Table of Contents:

  • Probability of Rolling Dice
  • Formula
  • Solved Problems
  • FAQs

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Probability of Rolling Dice - Grade 7 Math Worksheet PDF

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Probability of Rolling Dice

When rolling a standard six-sided die, the probability of rolling any given number is 1/6. This is because there are six equally likely outcomes, and each outcome has a probability of 1/6.

To calculate the probability of rolling a specific combination of numbers on multiple dice, you can use the multiplication rule of probability.

For example, if you roll two dice, the probability of rolling a 1 on the first die and a 2 on the second die is (1/6) * (1/6) = 1/36, since there are six possible outcomes for each die and they are independent events.

You can also calculate the probability of rolling a certain sum on multiple dice by listing all the possible outcomes and counting the number of outcomes that give the desired sum.

For example, the probability of rolling a sum of 7 on two dice is 6/36, or 1/6, since there are six possible ways to roll a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, and 6+1) out of a total of 36 possible outcomes.

Formula of Probability

Similarly, you can calculate the probability of rolling a sum greater than or equal to a certain value by counting the number of outcomes that meet the condition and dividing by the total number of outcomes.

For example, the probability of rolling a sum of 8 or higher on two dice is 10/36, or 5/18, since there are 10 possible ways to roll a sum of 8 or higher (2+6, 3+5, 4+4, 5+3, 6+2, 3+6, 4+5, 5+4, 6+3, and 6+4) out of a total of 36 possible outcomes.

Formula of Probability

The formula for calculating the probability of an event is:

P(A) = number of favorable outcomes / total number of possible outcomes

where P(A) is the probability of event A occurring.

For example, if you roll a standard six-sided die, the probability of rolling a 1 is:

P(rolling a 1) = 1 / 6

If you roll two dice and want to calculate the probability of rolling a 1 on the first die and a 2 on the second die, you can use the multiplication rule of probability:

P(rolling a 1 and a 2) = P(rolling a 1) * P(rolling a 2 given that a 1 was rolled)

Since the events are independent, the probability of rolling a 2 given that a 1 was rolled is also 1/6, so the formula becomes:

P(rolling a 1 and a 2) = (1/6) * (1/6) = 1/36

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Solved Problems of Probability of Rolling Dice

Problem 1: What is the probability of rolling a sum of 7 on two standard six-sided dice?

Solution: There are 6 possible outcomes for each die, so there are 6 x 6 = 36 total possible outcomes. To roll a sum of 7, there are 6 possible combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Therefore, the probability of rolling a sum of 7 is:

P(sum of 7) = number of favorable outcomes / total number of possible outcomes
P(sum of 7) = 6 / 36
P(sum of 7) = 1/6 or about 0.167

 

Problem 2: What is the probability of rolling a sum of 10 on three standard six-sided dice?

Solution: There are 6 possible outcomes for each die, so there are 6 x 6 x 6 = 216 total possible outcomes. To roll a sum of 10, there are several possible combinations: (1, 4, 5), (1, 5, 4), (2, 3, 5), (2, 4, 4), (2, 5, 3), (3, 2, 5), (3, 3, 4), (3, 4, 3), (3, 5, 2), (4, 2, 4), (4, 3, 3), (4, 4, 2), (5, 1, 4), (5, 2, 3), (5, 3, 2), and (5, 4, 1). Therefore, the probability of rolling a sum of 10 is:

P(sum of 10) = number of favorable outcomes / total number of possible outcomes
P(sum of 10) = 16 / 216
P(sum of 10) = 4/54 or about 0.074

 

Problem 3: What is the probability of rolling at least one 6 on three standard six-sided dice?

Solution: The probability of rolling at least one 6 on one die is 1 – the probability of not rolling a 6, which is 1 – (1/6) = 5/6. Therefore, the probability of not rolling a 6 on three dice is (5/6) x (5/6) x (5/6) = 125/216. The probability of rolling at least one 6 is the complement of this, which is 1 – 125/216 = 91/216 or about 0.421.

 

Problem 4: What is the probability of rolling a 6 on the first die and a 4 on the second die, given that the sum of the two dice is 10?

Solution: To roll a sum of 10, the only possible combination is (4, 6) or (6, 4). Therefore, the probability of rolling a 6 on the first die and a 4 on the second die, given that the sum of the two dice is 10, is:

P(6 on first die and 4 on second die | sum of 10) = P(6 on first die and 4 on second die and sum of 10) / P(sum of 10)
P(6 on first die and 4 on second die and sum of 10) = 1/36
P(sum of 10) = 2/36

Then probability will be 1/36 divided by 2/36 will be equal to 1/2.

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Probability of Rolling Dice FAQS

What is the probability of rolling a certain number on a single die?

The probability of rolling a certain number on a single die is 1/6, since there are six equally likely outcomes.

What is the probability of rolling the same number on two dice?

The probability of rolling the same number on two dice is 1/6, since there is only one favorable outcome out of six possible outcomes for each die.

What is the probability of rolling a sum of 6 on two dice?

There are several ways to roll a sum of 6 on two dice: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). Each of these outcomes has a probability of 1/36, so the probability of rolling a sum of 6 on two dice is 5/36.

What is the probability of rolling doubles on two dice?

The probability of rolling doubles on two dice is 1/6, since there is only one favorable outcome out of six possible outcomes for each die.

What is the probability of rolling a sum of 7 or 11 on two dice?

To roll a sum of 7, there are 6 possible combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). To roll a sum of 11, there are 2 possible combinations: (5, 6) and (6, 5). Each of these outcomes has a probability of 1/36, so the probability of rolling a sum of 7 or 11 on two dice is 8/36 or 2/9.

What is the probability of rolling a sum of 12 on two dice?

To roll a sum of 12, there is only one possible combination: (6, 6). This outcome has a probability of 1/36, so the probability of rolling a sum of 12 on two dice is 1/36.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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