Each of 2 players, independently, play a game 5 times, with each game having probability of success 0.40. What is the standard deviation

of the sum of the games they win

To find the standard deviation of the sum of games they win, we need to calculate the standard deviation of a binomial distribution since each game can be considered a success or failure with a given probability.

The formula to calculate the standard deviation of a binomial distribution is:

σ = sqrt(n * p * (1 - p))

Where:
- σ is the standard deviation
- n is the number of trials
- p is the probability of success in a single trial

In this case, each player plays the game 5 times, and the probability of success is 0.40. Therefore, the standard deviation can be calculated as:

For each player:
σ = sqrt(5 * 0.40 * (1 - 0.40))

Simplifying the equation:

σ = sqrt(5 * 0.40 * 0.60) = sqrt(1.20) ≈ 1.095

Thus, the standard deviation of the sum of games they win is approximately 1.095.