00:01
All right, for your question, you're rolling a die, and we have some payouts based on the numbers that you can roll.
00:06
If you roll an odd number, there's zero payout.
00:09
If you roll a two or a four, there's a $3 payout.
00:13
And if you roll a six, there's a $10 payout.
00:16
All right, so part a, we're trying to find the expected value of a roll.
00:21
Okay, to do that, we're going to need to know the probabilities of each of these outcomes.
00:25
The probability of getting an odd number on a die would be three out of six.
00:30
Or a half because there's six outcomes the numbers one through six and three of them are odd so three out of six was just one half all right so the two or four would happen two out of six times or one -third and the six would be one out of six times so i've now listed the probability for each possible outcome the expected value is to take those probabilities times the value of that outcome so we have one -half times zero plus one -third times three plus one -sixth times ten.
01:17
Now it tells you to round your answers to three decimal places.
01:22
This part's going to cancel out.
01:24
This would just be one, but that ten -sixth, ten -sixth is going to be a repeating decimal, and we will need to round.
01:34
So it's one -point -six repeating.
01:37
1 plus 1 .6 repeating would be 2 .667 rounded to 3 decimal places.
01:46
Part b of your question, you want to calculate the standard deviation...