Problema Solution
A six-sided die is weighted so that the probabilities of rolling a 1, 2, 3, or 4 are equal. The probabilities of rolling a 5 or a 6 are equal to each other. With this die, emma is three times more likely to roll a 6 than a 2. What is the probability that she will roll a 4? Express your answer as a common fraction.
Answer provided by our tutors
Let x be the probability of rolling a 4, or
P(4) = x
Then since the probabilities of rolling a 1, 2, 3, or 4 are equal we have:
P(1) = x, P(2) = x, P(3) = x, P(4) = x,
Emma is three times more likely to roll a 6 than a 2 means
P(6) = 3P(2)
P(6) = 3x
The probabilities of rolling a 5 or a 6 are equal to each other: P(5) = P(6) thus
P(5) = 3x
The sum of all these probabilities must equal 1, so
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
x + x + x + x + 3x + 3x = 1
by solving we find:
x = 1/10
click here to see the step by step solution of the equation:
the probability of rolling a 4 is 1/10.