Question
Watch Video
Show Examples
If a fair die is rolled 7 times, what is the probability, rounded to the nearest thousandth, of getting at least 6 threes?
Answer Attempt 1 out of 2
Submit Answer

Step 1 ：Calculate the probability of rolling a three on a fair die: \( p_{three} = \frac{1}{6} \)

Step 2 ：Calculate the probability of getting exactly 6 threes in 7 rolls using the binomial probability formula: \( prob_{6\_threes} = \binom{7}{6} \times \left( \frac{1}{6} \right)^6 \times \left( \frac{5}{6} \right)^1 \)

Step 3 ：Calculate the probability of getting exactly 7 threes in 7 rolls using the binomial probability formula: \( prob_{7\_threes} = \binom{7}{7} \times \left( \frac{1}{6} \right)^7 \times \left( \frac{5}{6} \right)^0 \)

Step 4 ：Sum the probabilities of getting exactly 6 threes and exactly 7 threes to find the total probability: \( total\_prob = prob_{6\_threes} + prob_{7\_threes} \)

Step 5 ：Round the total probability to the nearest thousandth: \( rounded\_total\_prob = 0.000 \)

Step 6 ：Final Answer: \(\boxed{0.000}\)