please help!! pretty please!!
i need to know how to this problem ASAP!
suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 1, nothing otherwise. what is your expected value?
Sure, I will explain how to solve this problem!
To find the expected value, you need to multiply each possible outcome by its probability and sum them up. In this case, we will consider the six possible outcomes when rolling a fair die: 1, 2, 3, 4, 5, and 6.
Since rolling a 5 or a 1 yields $3.00, the probabilities of these outcomes are 1/6 each. For the other four outcomes (2, 3, 4, 6), they have no monetary value, so their probabilities are each 1/6 as well.
To calculate the expected value, you can use the following formula:
Expected value = (Outcome 1 × Probability 1) + (Outcome 2 × Probability 2) + ... + (Outcome 6 × Probability 6)
In this case, the expected value will be:
Expected value = (3 × 1/6) + (0 × 1/6) + (0 × 1/6) + (0 × 1/6) + (3 × 1/6) + (0 × 1/6)
= (3/6) + (0/6) + (0/6) + (0/6) + (3/6) + (0/6)
= 6/6
= 1.00
Therefore, the expected value is $1.00.
I hope this explanation helps!