SOLUTION: A biased tetrahedral die with faces labelled 1,2,3 and 4 is rolled once. The chance of getting a '3' is twice that of getting a '1' . The chance of getting a '2' is thrice that of

Algebra ->  Probability-and-statistics -> SOLUTION: A biased tetrahedral die with faces labelled 1,2,3 and 4 is rolled once. The chance of getting a '3' is twice that of getting a '1' . The chance of getting a '2' is thrice that of       Log On


   



Question 1047071: A biased tetrahedral die with faces labelled 1,2,3 and 4 is rolled once. The chance of getting a '3' is twice that of getting a '1' . The chance of getting a '2' is thrice that of getting a '3' . There is an equal chance of getting a'2' and a '4' . Find the probability of getting a prime number.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
p%5B3%5D=2p%5B1%5D,
p%5B2%5D=+3p%5B3%5D,
p%5B2%5D+=+p%5B4%5D,
p%5B1%5D%2Bp%5B2%5D%2Bp%5B3%5D%2Bp%5B4%5D+=+1
p%5B2%5D=+3p%5B3%5D ===> p%5B3%5D=+p%5B2%5D%2F3;
p%5B3%5D=2p%5B1%5D ===> p%5B1%5D+=+p%5B3%5D%2F2+=+p%5B2%5D%2F6;

===> p%5B2%5D%2F6%2Bp%5B2%5D%2Bp%5B2%5D%2F3%2Bp%5B2%5D+=+1
<===> 5p%5B2%5D%2F2+=+1 ===> p%5B2%5D+=+2%2F5
===> p%5B4%5D+=+2%2F5, p%5B3%5D+=+2%2F15, and p%5B1%5D+=+1%2F15.

Therefore p%5Bprime%5D+=+p%5B2%5D%2Bp%5B3%5D+=+2%2F5%2B2%2F15+=+8%2F15