I got these obscure word problems today, I have a while to do them, but I wasn't given much direction and am not sure even where to start looking. They deal in probabilities and I believe it's going to involve some Calculus as my group was given these problems while taking calculus two.
I'm not asking for a solution, I was just wondering if someone thinks they know how they could be done, if they could perhaps offer a little direction in an approach.
Here they are:
(This one seems impossibly complicated.Jimmy and Dave have decided to create they're own duel. They decide to shoot one at a time firing one shot per turn at each other until one person is hit. Jimmy is the weaker shot with a 2/5 chance each shot of hittin Dave. Dave has a 2/3 chance of hitting Jimmy each shot. Jimmy, the weaker shot, will shoot first. What is the probability that Jimmy will win this game?
Please someone more schooled in probability please steer me in the right direction? I need to figure these out sometime in the future at least.A board game consists of four positions labeled A, B, C, and D. Whenever you reach position A or B, you roll some dice whose results determine what position you will move to next. Ah, but these dice are loaded.
From position A, there is a 1/4 chance of moving to position B, a 1/12 chance of moving to position C, and a 1/6 chance of moving to D.
From position B, there is a 1/3 chance of staying at B, there is a 1/3 chance of moving to position A, a 1/6 chance of moving to position C, and a 1/6 chance of moving to D.
Whenever you reach position C or D the game is over and you win some cake.
Suppose you begin the game at position A, what is the probability you end the game at position C