Die Roll & Coin Toss: Why 42 Possible Outcomes?

MHB
Thread starter Guest2
Start date Feb 7, 2016
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In summary, a die roll involves rolling a six-sided cube with numbers 1-6 on each face, and a coin toss involves flipping a coin with two possible outcomes: heads or tails. There are 42 possible outcomes for a die roll and coin toss because there are 6 possible outcomes for the die and 2 possible outcomes for the coin, resulting in 12 possible outcomes for each number on the die. The probability of getting a specific outcome is 1/42, or approximately 2.38%, since all outcomes have an equal chance of occurring. Using a die roll and coin toss in experiments is significant because they provide a simple and random way to generate outcomes, eliminating potential biases or patterns. The outcomes of a die roll

Feb 7, 2016

Guest2

A fair die is rolled twice. If the two results are the same, a coin is tossed. Why is the total number of different possible outcomes of this experiment $42$?

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Feb 7, 2016

Greg

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MHB

6 * 6 = 36, so 30 outcomes are a dice roll and 12 outcomes are a coin toss. 30 + 12 = 42.

Related to Die Roll & Coin Toss: Why 42 Possible Outcomes?

What is a die roll and coin toss?

A die roll involves rolling a six-sided cube with numbers 1-6 on each face, while a coin toss involves flipping a coin with two possible outcomes: heads or tails.

Why are there 42 possible outcomes for a die roll and coin toss?

There are 42 possible outcomes because the die has 6 possible outcomes and the coin has 2 possible outcomes. When we multiply these numbers together, we get 12 possible outcomes for each number on the die. Therefore, 6 x 12 = 42 possible outcomes for a die roll and coin toss.

What is the probability of getting a specific outcome?

The probability of getting a specific outcome is 1/42, or approximately 2.38%. This is because all outcomes have an equal chance of occurring, and there are 42 possible outcomes.

What is the significance of using a die roll and coin toss in experiments?

Dice and coins are often used in experiments because they provide a simple and random way to generate outcomes. This helps eliminate any potential biases or patterns in the results.

Can the outcomes of a die roll and coin toss be manipulated?

No, the outcomes of a die roll and coin toss are completely random and cannot be manipulated. As long as the die and coin are properly balanced, each outcome has an equal chance of occurring.