Try your biased luck

Probability Level 2

A six-sided dice is biased so that the probability for a particular face to show is proportional to the number of dots on that face.

When the dice is rolled, what is the probability that we get an even number?

4 7 \frac{4}{7} 3 5 \frac{3}{5} 1 2 \frac{1}{2} 2 3 \frac{2}{3}

Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

Ramesh Goenka
Mar 26, 2015

4 Helpful 0 Interesting 1 Brilliant 0 Confused
Brock Brown
Mar 28, 2015

solution solution

Here's a Python simulation of what happens in the gif:

Python 2.7: 

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from fractions import Fraction as frac
dice = xrange(1,7)
# count every dot
dots = 0
for side in dice:
    dots += side
# find probabilities of even sides
even_probs = []
for side in dice:
    if side % 2 == 0:
        even_probs.append(frac(side,dots))
# add them up
print "Answer:", sum(even_probs)

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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