# How to obtain this particular probability distribution and standard deviation?

Currently, I am studying statistics as an undergraduate. Our lecture today finished with information about obtaining probability distributions and expected values (using binomial and geometric distributions).

Later that day, after throwing some snow with some friends, I figured it would be neat to use what I learned to create a statistical project from throwing snowballs.

# My Experiment

Three individuals stand in a triangle. Each individual has a die and a full deck of cards (excluding Jokers)

Each person rolls their dice and flips a card at the same time. If the die lands on an even number, they throw a snowball to the individual at their left. If the card lands on an odd-valued card, the individual throws a snowball at the individual to their right.

Once someone has been hit by 5 snowballs, that player is no longer in the match. However, once I started on this, I could not figure out how to calculate a probability distribution. I realized that, although it may seem easy at first, the hard part is accounting for whenever an individual may be eliminated. Also, I can't figure out the standard deviation or expected value for the random variable 'x' which I chose to represent the chance of an individual being hit.

I would definitely be able to calculate this if this experiment was altered for only two individuals, but how can I use statistics to include the third individual? I really do enjoy statistics, and it's something I love to test. If anyone can guide me in the right direction, that would be appreciated!

• Is the card considered only if the die lands on an odd number? – Jack's wasted life Jan 27 '16 at 2:30
• @Jack'swastedlife Yes indeed; however, I'm willing to modify the rules of my experiment to make the calculations more 'doable'. It's mainly the calculations I am interested in performing – Digital Veer Jan 27 '16 at 2:31