Question

Chance of winning at "craps." A version of the dice game "craps" is played in the following manner. A player starts by rolling two balanced dice. If the roll (the sum of the two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or a 3 (called craps), the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). a) If the player throws a total of 4 on the first roll, what's the probability that the game ends (win or lose) on the next roll?

          Chance of winning at "craps." A version of the dice game "craps"
is played in the following manner. A player starts by rolling two
balanced dice. If the roll (the sum of the two numbers showing on
the dice) results in a 7 or 11, the player wins. If the roll
results in a 2 or a 3 (called craps), the player loses. For any
other roll outcome, the player continues to throw the dice until
the original roll outcome recurs (in which case the player wins) or
until a 7 occurs (in which case the player loses).
a) If the player throws a total of 4 on the first roll, what's
the probability that the game ends (win or lose) on the next
roll?

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Added by Judy S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Avi Zellman

03/02/2022

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The player rolls two dice and gets a total of 4 on the first roll. We need to find the probability that the game ends on the next roll, either by rolling a 4 (win) or a 7 (lose). Show more…

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Chance of winning at "craps." A version of the dice game "craps" is played in the following manner. A player starts by rolling two balanced dice. If the roll (the sum of the two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or a 3 (called craps), the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). a) If the player throws a total of 4 on the first roll, what's the probability that the game ends (win or lose) on the next roll?

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Transcript

00:01 So we're given a problem that's looking at the game of craps.

00:04 The game of craps, you've got two six -sided dice where you throw them.

00:09 And based on how they land, you either can win immediately or lose immediately or it can result in more roles.

00:18 So in our situation, we're given that the person rolls first role is equal to a sum of a four.

00:30 And that means that in order for the person to win on their second role, they need to roll another four.

00:38 That would be their win.

00:40 But if they roll a seven, then that means that they lose.

00:47 Okay? so the question is, well, what's the probability of someone, of the game ending, either rolling a four or a seven on their second rule? so we can do this by setting up just a basic chart.

01:00 To help us break down all these possibilities.

01:04 So there's two dice.

01:07 Each of them have six sides.

01:09 So we can put them out here.

01:11 Whoops.

01:14 Three, four, five, six.

01:17 And then we can just see the sum in each of these.

01:20 So maybe i'll use a different.

01:23 Let me use blue in the middle here so you can see it more clearly.

01:26 Three, four, five, six, seven.

01:30 Then you'll see the pattern show up pretty quickly.

01:33 Of how this table kind of works...

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