What is the probability of a die not coming up six, six times in a row?
How do I solve that problem?
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To solve the problem, we need to understand a few concepts. Let's break it down step by step:
1. Probability of rolling any specific number on a fair six-sided die:
Since a die has six sides, each with an equal chance of landing facing up, the probability of rolling a specific number, such as six, is 1/6.
2. Probability of not rolling a specific number on a single roll:
The probability of not rolling a specific number is the complement of rolling that number, which means it's 1 minus the probability of rolling it. In this case, the probability of not rolling a six is 1 - (1/6) = 5/6.
3. Probability of not rolling a specific number, repeatedly:
To find the probability of not rolling a specific number multiple times in a row, we multiply the probabilities of not rolling that number in each individual roll.
Now, we can calculate the probability of a die not coming up six, six times in a row:
(P(not rolling a six))^6 = (5/6)^6 ≈ 0.3349
Therefore, the probability of a die not coming up six, six times in a row is approximately 0.3349 or 33.49%.
To solve it mathematically, you raised the probability of not rolling a six (5/6) to the power of 6 because you want to calculate the probability of this outcome happening in six consecutive rolls.