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A die is rolled four times, what is the probability of obtaining exactly one six
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To find the probability of obtaining exactly one six when rolling a die four times, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes when rolling a die four times: Each roll has 6 possible outcomes (numbers 1 to 6), so the total number of outcomes for four rolls is 6^4 = 1296.
Number of favorable outcomes: We want to obtain exactly one six, which means there are four rolls and one of them results in a six. We have four different positions where the six can occur, so we multiply the number of ways to get a six on one roll (1) by the number of ways to get any number other than six on the remaining three rolls (5^3 = 125).
Number of favorable outcomes = 4 * 1 * 5^3 = 500
Now we can calculate the probability:
Probability of obtaining exactly one six = Number of favorable outcomes / Total number of possible outcomes
= 500 / 1296
= 25/ 64.
So, the probability of obtaining exactly one six when rolling a die four times is 25/64.
To find the probability of obtaining exactly one six when rolling a die four times, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes when rolling a die four times: Since each roll of the die has 6 possible outcomes (numbers 1 through 6), the total number of possible outcomes when rolling a die four times is 6 × 6 × 6 × 6 = 6^4 = 1296.
Now, let's consider the number of favorable outcomes, i.e., the number of ways we can obtain exactly one six in four rolls.
To obtain exactly one six, we have four possible positions where the six could occur: the first roll, second roll, third roll, or fourth roll.
Case #1: Six on the first roll and not on the other three rolls
In this case, we can have any of the numbers 1 through 5 on the remaining three rolls. So, the number of favorable outcomes is 1 × 5 × 5 × 5 = 125.
Case #2: Six on the second roll and not on the other three rolls
Similar to Case #1, we have 5 possible numbers on the first roll, 1 six on the second roll, and 5 possible numbers on the remaining two rolls. Therefore, the number of favorable outcomes is 5 × 1 × 5 × 5 = 125.
Case #3: Six on the third roll and not on the other three rolls
Following the same logic, the number of favorable outcomes is 5 × 5 × 1 × 5 = 125.
Case #4: Six on the fourth roll and not on the other three rolls
Again, the number of favorable outcomes is 5 × 5 × 5 × 1 = 125.
Adding up the favorable outcomes from all four cases, we get a total of 125 + 125 + 125 + 125 = 500
Therefore, the probability of obtaining exactly one six when rolling a die four times is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 500 / 1296 = 125/324 ≈ 0.386 or 38.6% (rounded to one decimal place).
So, the probability of obtaining exactly one six is approximately 0.386 or 38.6%.
The die has 6 sides, the probability of rolling a six when the die is rolled once is 1/6.
When rolled 4 times, each time has a probability of 1/6.
So,
1/6 * 1/6 *1/6 *1/6 = 1/1296
The above answer is not quite right.
"The die has 6 sides, the probability of rolling a six when the die is rolled once is 1/6" is true. So let, p = 1/6. We are looking for the probability of exactly one success in 4 rolls. Using the Bernoulli trials method,
your answer will be .386