SOLUTION: A and B play for a prize to win 1000 Birr. A is to throw a die first and to win if he throws 6. If A fails, B is to throw and to win if he throws 5 or 6. If B fails, A is to throw

Algebra ->  Probability-and-statistics -> SOLUTION: A and B play for a prize to win 1000 Birr. A is to throw a die first and to win if he throws 6. If A fails, B is to throw and to win if he throws 5 or 6. If B fails, A is to throw       Log On


   

Question 676511: A and B play for a prize to win 1000 Birr. A is to throw a die first and to win if he throws 6. If A fails, B is to throw and to win if he throws 5 or 6. If B fails, A is to throw again to win if throws 4, 5 or 6, and so on.
a. Find the total probabilities of A’s success

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
1st throw: 1/6 probability A wins
.
2nd: 1- 1/6 = 5/6
5/6 * 2/6 = 5/18 prob B wins
.
3rd 1-(1/6 + 5/18)=5/9
5/9 * 3/6 = 5/18 prob A wins
.
4th 1-(1/6 + 5/18 + 5/18)=5/18
5/18 * 4/6 =5/27 prob B wins
.
5th 1-(1/6 + 5/18 + 5/18 + 5/27)=5/54
5/54 * 5/6 = 25/324 Prob A wins
.
1-(1/6 + 5/18 + 5/18 + 5/27 + 25/324)=5/324 prob B wins.
.
1/6 + 5/18 + 25/324 = 169/324 the total probabilities of A’s success.
.
Ed