i got the following wrong, but don't know what I did wrong-
die rolled 30 times, what is the expected value that a 5 will appear. I thought 3.5, but was told wrong. Help!
See your later post.
To determine the expected value of a specific outcome, such as rolling a 5 on a die, you need to consider the probability of that outcome occurring.
In this case, you need to calculate the probability of rolling a 5 on a fair six-sided die. Each roll of the die has an equal probability of 1/6 of landing on any specific number (since there are six sides on the die and all numbers are equally likely).
Now, since you rolled the die 30 times, you can think of each roll as an independent event. The probability of rolling a 5 on any individual roll is still 1/6.
To calculate the expected value, you multiply the probability of each outcome by its value and sum them up. In this case, the value of rolling a 5 is 5. So, the expected value of rolling a 5 once can be calculated as (1/6) * 5 = 5/6.
Since you rolled the die 30 times, you can simply multiply the expected value of rolling a 5 once by the number of rolls, which gives you:
(5/6) * 30 = 25
Therefore, the expected value of rolling a 5 in 30 rolls of a fair six-sided die is 25, not 3.5 as you initially thought.