Question

A gambling game works as follows: you flip a fair coin four times (one after another). you will be paid $4 if you get 0 or 1 heads and $1 if you get 3 heads. otherwise, you have to pay $2.50.

Answer 1

The student's question involves calculating the expected value of a probabilistic gambling game involving coin flips, a common high school level math problem in the field of statistics.

Step-by-step explanation:

The student's question pertains to the expected value of a given gambling game with four separate outcomes depending on the number of heads flipped in a sequence of coin tosses. This involves probability and statistics, concepts usually covered in high school math curricula. The overall problem is to calculate the expected profit or loss when playing this game multiple times.

Expected value (EV) is a statistical concept used to determine the average outcome of a random event over the long term. To calculate EV, you multiply each possible outcome by its probability and sum these products. The law of large numbers states that over many trials, the actual results will converge to the expected value.

To compute the expected value for the provided game, you would identify each outcome (0, 1, 3 heads, or other), calculate its probability, multiply each by the corresponding payoff, and sum them. You must also consider losses, as the player must pay $2.50 in some scenarios. The expected value will indicate whether or not this game is beneficial to play in the long run.