1.Master of Magic - Heroes: Apparently, video games are becoming a more popular 'sport' these days.I have been playing a lot of 'Master of Magic' a classic video game from 1996.It is clearly a dated video game, but I still think it may become the next spectator sport.I figure that, if I get really, really good at playing Master of Magic, it will be my shot at fame and fortune.

In the game, the player is a wizard who directs armies made up of individual units and spells in combat against up to four other wizards controlled by the computer.The goal is to 'take over the world' which means eliminating the other wizards.The computer randomly determine the outcomes of spells and combat.

This time, I was about to be attacked by 7 enemy skeleton units.I have two heroes I could use to deal with them:

Tony the Barbarian has a magical Ethereal Axe of Vanquishing that is specifically enchanted to eliminate the undead.To destroy an enemy, Tony must hit the enemy with his axe (i.e. roll a 17 or higher on a 20-sided dice) and then the enemy must fail its saving throw (i.e. roll below a 16 on a 20 sided dice).Unfortunately, If Tony misses the enemy or the enemy succeeds in its saving throw, the axe does no damage.The good news is that Tony has 50 turns and he can take one swing each turn (naturally, he can only eliminate one enemy unit per turn.)After his 50 turns, he will be exhausted and forced to retreat from battle.

Nicole the Mage has a Wand of Fireballs.With her magic wand, she is capable of delivering a blast of intense flames, possibly destroying a skeleton unit where it stands.She can use the wand 15 times, and each time it has a 50% chance completely incinerating a single enemy unit (if a unit is not incinerated, it is unharmed.)After her wand is used up, she has to fly away from the battle to safety (she is a mage, you know!)

a.Which hero should I send in to battle the skeletons? Be sure to justify your decision using techniques from class.

b.How likely is it that my side will win the battle?

c.Let's suppose, to be fair, I flipped a coin to pick which hero I would send to battle the skeletons.Even though my selection process was based on a coin toss, my hero won!What is the probability that Tony was picked for this battle?