David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: Probability Games and Play, Exercise 26: Practice 6

Ringball is a traditional South African that is related both basketball and netball. Play takes place on a field(indoors and outdoors) where players pass a ball from one teammate to another and then, hopefully, throw the ball through a hoop on a goalpost. Suppose a player makes $75\%$ of her shots when she tries to score. What is the experimental probability that she will score on three consecutive shots? Round up to three places.

In a game of Skunk, two players get five rounds to earn the most points. During a turn, the player rolls a six-sided die. If the player rolls a $1$, the player gets $0$ points and the turn is over, If the player rolls a $2, 3, 4, 5$ or $6$, then the value is recorded as that many points. If the player earned points, there is a decision to make: the player can take risk and roll again, or keep the value earned. If the player rolls again, the value is added to the recorded score. If the player rolls a $1$, the accumulated score goes down to zero. Write down the sample space for all of possible outcomes of four rolls of the die.

In a game of Skunk, two players get five rounds to earn the most points. During a turn, the player rolls a six-sided die. If the player rolls a $1$, the player gets $0$ points and the turn is over, If the player rolls a $2, 3, 4, 5$ or $6$, then the value is recorded as that many points. If the player earned points, there is a decision to make: the player can take risk and roll again, or keep the value earned. If the player rolls again, the value is added to the recorded score. If the player rolls a $1$, the accumulated score goes down to zero. Find $P(>1>1, \mathrm{then}>1)$. Round upto three decimal places.

In a game of Skunk, two players get five rounds to earn the most points. During a turn, the player rolls a six-sided die. If the player rolls a $1$, the player gets $0$ points and the turn is over, If the player rolls a $2, 3, 4, 5$ or $6$, then the value is recorded as that many points. If the player earned points, there is a decision to make: the player can take risk and roll again, or keep the value earned. If the player rolls again, the value is added to the recorded score. If the player rolls a $1$, the accumulated score goes down to zero. Find $\left(P>1, >1, >1, \mathrm{then} >1\right)$. Round up to three decimal places.

In a game of Skunk, two players get five rounds to earn the most points. During a turn, the player rolls a six-sided die. If the player rolls a $1$, the player gets $0$ points and the turn is over, If the player rolls a $2, 3, 4, 5$ or $6$, then the value is recorded as that many points. If the player earned points, there is a decision to make: the player can take risk and roll again, or keep the value earned. If the player rolls again, the value is added to the recorded score. If the player rolls a $1$, the accumulated score goes down to zero. Based on your calculations, is it wise for a player to continue risking rolling again? Use your calculations in your explanation.

In a game of Skunk, two players get five rounds to earn the most points. During a turn, the player rolls a six-sided die. If the player rolls a $1$, the player gets $0$ points and the turn is over, If the player rolls a $2, 3, 4, 5$ or $6$, then the value is recorded as that many points. If the player earned points, there is a decision to make: the player can take risk and roll again, or keep the value earned. If the player rolls again, the value is added to the recorded score. If the player rolls a $1$, the accumulated score goes down to zero. 

Suppose you played Skunk with your friend Robin, and their and second round results were those shown in those two tables.

Examining round $1$, what is the theoretical probability of rolling $2$, then $4$ and then $5$?

In a game of Skunk, two players get five rounds to earn the most points. During a turn, the player rolls a six-sided die. If the player rolls a $1$, the player gets $0$ points and the turn is over, If the player rolls a $2, 3, 4, 5$ or $6$, then the value is recorded as that many points. If the player earned points, there is a decision to make: the player can take risk and roll again, or keep the value earned. If the player rolls again, the value is added to the recorded score. If the player rolls a $1$, the accumulated score goes down to zero. 

Suppose you played Skunk with your friend Robin, and their and second round results were those shown in those two tables.

Examining round $2$, what is the theoretical  probability of rolling $6, 5, 2, 4$ and then $1$?

In a game of Skunk, two players get five rounds to earn the most points. During a turn, the player rolls a six-sided die. If the player rolls a $1$, the player gets $0$ points and the turn is over, If the player rolls a $2, 3, 4, 5$ or $6$, then the value is recorded as that many points. If the player earned points, there is a decision to make: the player can take risk and roll again, or keep the value earned. If the player rolls again, the value is added to the recorded score. If the player rolls a $1$, the accumulated score goes down to zero. 

Suppose you played Skunk with your friend Robin, and their and second round results were those shown in those two tables.

Before starting round $3$, you have accumulated $11$ points. On your first roll in this round, you've rolled a $2$. Should you stop rolling? Is it worth the risk to roll again to widen your new lead?