Question

felicia has a stack of 10 cards. each card is labeled with a number in the ramge 1 throguh 10 and no two cards have the same number. she picks three cards at random from the stack the stack adds the numbers on the three cards. what is the expected valu of the sum

Answer 1

The expected value of the sum of the three randomly chosen cards is 6.05.

Step-by-step explanation:

The expected value of the sum of the three cards can be calculated by finding the average sum of all possible outcomes. In this case, there are 10 cards and any combination of three cards can be chosen, so the total number of possible outcomes is the number of ways to choose 3 cards from 10, which is denoted as C(10, 3) or 10 choose 3.

Using the formula for combinations, C(10, 3) = 10! / (3!(10-3)!) = 120.

Now, we need to find the sum of all possible outcomes and divide it by the total number of outcomes. Since each card is labeled with a unique number, the sum of the numbers on the three cards can range from the smallest possible sum (1+2+3=6) to the largest possible sum (8+9+10=27). So, the sum of all possible outcomes can be calculated as:

(6 + 7 + 8 + ... + 27) = (6 + 27)(22)/2 = 33 * 22 = 726

Finally, we divide the sum of all possible outcomes by the total number of outcomes:

Expected value = 726/120 = 6.05