Part 1: you are playing a game of russian roulette with me. i put it 2 bullets in consecutive chambers, spin it, and take my turn. i survived the round, and now it's your turn. you can either take the gun as it is, or spin the chamber to make it random again. which option gives you a better chance of surviving?

part 2: what would the answer be if there was only 1 bullet instead?

1. The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.

2. The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.

Step-by-step explanation:

1. Which option gives you a better chance of surviving?

Let's assume the gun has six chambers, so the probabilities are:

Number of bullets remaining/Number of chambers

For the first attempt, probabilities are = 2/6 or 33%

For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 2/5 or 40%

On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 2/6 or 33%

The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.

2. What would the answer be if there was only 1 bullet instead?

Number of bullets remaining/Number of chambers

For the first attempt, probabilities are = 1/6 or 17%

For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 1/5 or 20%

On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 1/6 or 17%

The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages