Mixing
You roll two fair dice. What is the probability to win the game based on restrictions over the sum of the...
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You roll two fair dice. If the sum of the numbers shown is $7$ or $11$, you win; if it is $2$, $3$, or $12$, you lose. If it is any other number $j$, you continue to roll two dice until the sum is $j$ or $7$, whichever is sooner. If it is $7$, you lose; if it is $j$, you win.
(a) What is the probability $p$ that you win?
(b) What is the probability that you win on or before the second roll?
(c) What is the probability that you win on or before the third roll?
(d) What is the probability that you win if, on the first roll
(d.1) The first die shows 2?
(d.2) The first die shows 6?
(e) If you could fix the number to be shown by one die of the two on the first roll, what number would you choose?
MY ATTEMPT
Unfortunately, I do not know how tackle the exercise. I am aware that it may be needed to use conditional probability, but I am unable to describe properly the involved events. However, it is not a homework problem. I am really interested in the response of these questions. Thank you in advance.
probability probability-theory conditional-probability dice
asked Jan 13 at 19:27
user1337user1337
46110
$endgroup$
add a comment |
$begingroup$
You roll two fair dice. If the sum of the numbers shown is $7$ or $11$, you win; if it is $2$, $3$, or $12$, you lose. If it is any other number $j$, you continue to roll two dice until the sum is $j$ or $7$, whichever is sooner. If it is $7$, you lose; if it is $j$, you win.
(a) What is the probability $p$ that you win?
(b) What is the probability that you win on or before the second roll?
(c) What is the probability that you win on or before the third roll?
(d) What is the probability that you win if, on the first roll
(d.1) The first die shows 2?
(d.2) The first die shows 6?
(e) If you could fix the number to be shown by one die of the two on the first roll, what number would you choose?
MY ATTEMPT
Unfortunately, I do not know how tackle the exercise. I am aware that it may be needed to use conditional probability, but I am unable to describe properly the involved events. However, it is not a homework problem. I am really interested in the response of these questions. Thank you in advance.
probability probability-theory conditional-probability dice
asked Jan 13 at 19:27
user1337user1337
46110
$endgroup$
$begingroup$
Try a simpler game. What if you only had one die, and you lost on 1 and won on 5 or 6 and otherwise threw again?
$endgroup$
– Arthur
Jan 13 at 19:37
$begingroup$
vc.bridgew.edu/cgi/…
$endgroup$
– amd
Jan 13 at 20:29
$begingroup$
Try solving parts (b) and (c) first.
$endgroup$
– amd
Jan 14 at 1:23
add a comment |
$begingroup$
You roll two fair dice. If the sum of the numbers shown is $7$ or $11$, you win; if it is $2$, $3$, or $12$, you lose. If it is any other number $j$, you continue to roll two dice until the sum is $j$ or $7$, whichever is sooner. If it is $7$, you lose; if it is $j$, you win.
(a) What is the probability $p$ that you win?
(b) What is the probability that you win on or before the second roll?
(c) What is the probability that you win on or before the third roll?
(d) What is the probability that you win if, on the first roll
(d.1) The first die shows 2?
(d.2) The first die shows 6?
(e) If you could fix the number to be shown by one die of the two on the first roll, what number would you choose?
MY ATTEMPT
Unfortunately, I do not know how tackle the exercise. I am aware that it may be needed to use conditional probability, but I am unable to describe properly the involved events. However, it is not a homework problem. I am really interested in the response of these questions. Thank you in advance.
probability probability-theory conditional-probability dice
asked Jan 13 at 19:27
user1337user1337
46110
$endgroup$
You roll two fair dice. If the sum of the numbers shown is $7$ or $11$, you win; if it is $2$, $3$, or $12$, you lose. If it is any other number $j$, you continue to roll two dice until the sum is $j$ or $7$, whichever is sooner. If it is $7$, you lose; if it is $j$, you win.
(a) What is the probability $p$ that you win?
(b) What is the probability that you win on or before the second roll?
(c) What is the probability that you win on or before the third roll?
(d) What is the probability that you win if, on the first roll
(d.1) The first die shows 2?
(d.2) The first die shows 6?
(e) If you could fix the number to be shown by one die of the two on the first roll, what number would you choose?
MY ATTEMPT
Unfortunately, I do not know how tackle the exercise. I am aware that it may be needed to use conditional probability, but I am unable to describe properly the involved events. However, it is not a homework problem. I am really interested in the response of these questions. Thank you in advance.
probability probability-theory conditional-probability dice
probability probability-theory conditional-probability dice
asked Jan 13 at 19:27
user1337user1337
46110
asked Jan 13 at 19:27
user1337user1337
46110
asked Jan 13 at 19:27
user1337user1337
46110
asked Jan 13 at 19:27
user1337user1337
46110
asked Jan 13 at 19:27
user1337user1337
46110
46110
$begingroup$
Try a simpler game. What if you only had one die, and you lost on 1 and won on 5 or 6 and otherwise threw again?
$endgroup$
– Arthur
Jan 13 at 19:37
$begingroup$
vc.bridgew.edu/cgi/…
$endgroup$
– amd
Jan 13 at 20:29
$begingroup$
Try solving parts (b) and (c) first.
$endgroup$
– amd
Jan 14 at 1:23
add a comment |
$begingroup$
Try a simpler game. What if you only had one die, and you lost on 1 and won on 5 or 6 and otherwise threw again?
$endgroup$
– Arthur
Jan 13 at 19:37
$begingroup$
vc.bridgew.edu/cgi/…
$endgroup$
– amd
Jan 13 at 20:29
$begingroup$
Try solving parts (b) and (c) first.
$endgroup$
– amd
Jan 14 at 1:23
$begingroup$
Try a simpler game. What if you only had one die, and you lost on 1 and won on 5 or 6 and otherwise threw again?
$endgroup$
– Arthur
Jan 13 at 19:37
$begingroup$
Try a simpler game. What if you only had one die, and you lost on 1 and won on 5 or 6 and otherwise threw again?
$endgroup$
– Arthur
Jan 13 at 19:37
$begingroup$
vc.bridgew.edu/cgi/…
$endgroup$
– amd
Jan 13 at 20:29
$begingroup$
vc.bridgew.edu/cgi/…
$endgroup$
– amd
Jan 13 at 20:29
$begingroup$
Try solving parts (b) and (c) first.
$endgroup$
– amd
Jan 14 at 1:23
$begingroup$
Try solving parts (b) and (c) first.
$endgroup$
– amd
Jan 14 at 1:23
add a comment |
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$begingroup$
Try a simpler game. What if you only had one die, and you lost on 1 and won on 5 or 6 and otherwise threw again?
$endgroup$
– Arthur
Jan 13 at 19:37
$begingroup$
vc.bridgew.edu/cgi/…
$endgroup$
– amd
Jan 13 at 20:29
$begingroup$
Try solving parts (b) and (c) first.
$endgroup$
– amd
Jan 14 at 1:23