When tossing an unbiased die, each face (including the six) has an equal probability of landing face up. This probability is
1/6, since there are six faces on a standard die.
To find the mean number of sixes obtained when the die is tossed 500 times, we can use the formula for expected value, which is given by:
Expected Value (E) = n * p
where:
- n = number of trials (in this case, the number of tosses)
- p = probability of success on each trial (the chance of rolling a six)
Here, n is 500 and p is 1/6:
E = 500 * (1/6)
Calculating this gives:
E = 500/6 ≈ 83.33
This means that if you were to toss an unbiased die 500 times, you would expect to roll a six approximately 83.33 times. In practical terms, this suggests that over a large number of trials, the number of sixes should average out to around 83 or 84. Keep in mind that while this is the expected mean, actual results can vary due to the randomness of each toss.