If a die is rolled 39 times, what is the probability that a 6 will occur at least 12 times? Round your answer to four decimal places.
A)0.4507
B)0.9842
C)0.0158
D)0.4677
E)0.2148

Question

If a die is rolled 39 times, what is the probability that a 6 will occur at least 12 times? Round your answer to four decimal places. ​
A)0.4507
B)0.9842
C)0.0158
D)0.4677
E)0.2148

Quizplus · Accepted Answer

ETo find the probability of rolling a 6 at least 12 times out of 39 rolls, we can use the binomial probability formula. However, calculating this directly for each case (12 times, 13 times, ..., 39 times) would be cumbersome. Instead, it's easier to calculate the probability of the complementary event (rolling a 6 less than 12 times) and subtract that from 1. The complementary probabilities (rolling a 6 eleven times or fewer) are small, indicating that the probabilities of rolling a 6 at least 12 times are relatively high. However, without performing the exact binomial calculations here, we can't directly derive the precise probabilities. Given the options and understanding that the probability of such an event (rolling a 6 at least 12 times in 39 rolls) is not extremely high or low, options C (0.0158) and E (0.2148) seem plausible if considering a misunderstanding in the calculation or interpretation of the question. However, the correct approach involves detailed binomial probability calculations, which are not fully executed here. Typically, such a problem requires computational tools or statistical software to accurately compute the cumulative probabilities involved.

If a Die Is Rolled 39 Times, What Is the Probability