Question

I need some help with statistics!

Answer 1

I attached a document but I don't know if it will open so here is the question:
(I have a-c done I'm stuck on part d)
Casinos rely on the laws of probability and expected values of random variables to
guarantee them profits on a daily basis. Some individuals will walk away very wealthy,
while others will leave with nothing but memories. Let’s take a look at the game of CRAPS:

Roll a pair of six-sided dice. If the sum is 7 or 11, you win. If the sum is 2, 3, or 12, you
lose. If the sum is any other number, you roll again. In fact, you continue throwing the
dice until you either roll that same number again (WIN!) or roll a 7 (LOSE!).

a. What is the probability that you obtain a sum of 7 or a sum of 11 on the first roll?
(Remember the sample space for rolling 2 dice.)



b. What is the probability that you obtain a sum of 2, 3, or 12 on the first roll?



c. What is the probability you will have to roll again?
(You got something other than a 7, 11, 2, 3, or 12 on the first roll.)



d. The probability of winning CRAPS is 0.493 (based on the calculations above and geometric probability of “waiting” until the same number appears.) Knowing the probability is 0.493 for winning one game of CRAPS, suppose you feel adventurous, and play 2 games.
Find each probability using the rules learned in this chapter.

i. What is the probability that you win both games?
(Be careful, your probability should not be getting larger…..)



ii. What is probability you win the first game and lose the second?




iii. What is the probability you lose both games?




iv. Why do casinos make money off of this game???

Answer 2

The events 'win the first game' and 'win the second game' are independent. Therefore the probability of winning both games is:
\[\large P(win\ both)=0.493\times0.493=you\ can\ calculate\]

Answer 3

thanks!

Answer 4

You're welcome :)
Can you find the solution to d.ii using the same reasoning as for d. i ?