SOLUTION: A peculiar die has the following properties: on any roll the probability of rolling either a 2, a 3, or a 5 is 1/2, just as it is with an ordinary die. Moreover, the probability of

Algebra ->  Probability-and-statistics -> SOLUTION: A peculiar die has the following properties: on any roll the probability of rolling either a 2, a 3, or a 5 is 1/2, just as it is with an ordinary die. Moreover, the probability of      Log On


   

Question 945915: A peculiar die has the following properties: on any roll the probability of rolling either a 2, a 3, or a 5 is 1/2, just as it is with an ordinary die. Moreover, the probability of rolling either a 5, a 6, or a 4 is again 1/2. However, the probability of rolling a 5 is 3/16, not 1/6 as one would expect of an ordinary fair die.
From what you know about this peculiar die, compute
A) the probability of rolling either a 2, a 3, or a 1;
B) the probability of rolling anything but a 1.
Answer by mathmate(429) About Me  (Show Source):
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Given
An unbalanced die such that
1) P(2)+P(3)+P(5) = 1%2F2
2) P(5)+P(6)+P(4) = 1%2F2
3) P(5) = 3%2F16
Find
A) P(2)+P(3)+P(1) = ?
B) P(2)+P(3)+P(4)+P(5)+P(6) = ?

Solution
Given P(5) = 3%2F16, then
P(2)+P(3)+P(5) = P(2)+P(3)+ 3%2F16 = 1%2F2
which means
P(2)+P(3) = 1%2F2+-+3%2F16 = 5%2F16
Similarly,
using
P(5)+P(6)+P(4) = 1%2F2
we find
P(6)+P(4) = 1%2F2+-+3%2F16 = 5%2F16
Since there are only six faces, we calculate P(1) as follows:
A)
P(1) = 1-( P(2)+P(3) + P(5) + P(6)P(6)+P(4) ) = 1-%285%2F16%2B3%2F16%2B5%2F16%29 = 3%2F16

B)
P(2)+P(3)+P(5)+P(6)P(6)+P(4) = 1-P(1) = 1-3%2F16 = 13%2F16