Consider a disk and spinner with four equal sectors marked with the numerals 1, 2, 3, and 4.
What is the expected value for a single spin?
If the spinner is spun three times, what is the expected value for the sum of the three numbers spun?
expected value = 1/4(1) + 1/4(2) + 1/4(3) + 1/4(4) = 5/2 or 2.5
So for 3 spins wouldn't it be 7.5 ?
You win $4 if you flip a coin twice and get tails both times. For any other outcome you get nothing. What is the expected value?
it wouldn't be because if you do the math it is really close.
To find the expected value for a single spin, we need to calculate the average value that can be obtained from the possible outcomes.
In this case, the possible outcomes are the numbers 1, 2, 3, and 4, each with an equal probability of 1/4.
To calculate the expected value, multiply each outcome by its probability and sum them up:
Expected value = (1 * 1/4) + (2 * 1/4) + (3 * 1/4) + (4 * 1/4)
Simplifying this equation:
Expected value = 1/4 + 1/2 + 3/4 + 1
Expected value = 7/2 = 3.5
Therefore, the expected value for a single spin is 3.5.
Now let's move on to the case of spinning the spinner three times.
To find the expected value for the sum of the three numbers spun, we need to think about how the spinner behaves each time it is spun and add up the expected values.
Since each spin is independent and has an expected value of 3.5 (as calculated previously), we can simply multiply the expected value of a single spin by the number of spins:
Expected value for the sum of three numbers = 3.5 * 3
Expected value for the sum of three numbers = 10.5
Therefore, the expected value for the sum of the three numbers spun is 10.5.