Julia made a die for a game. It had 5 faces, labeled 1-5. Because of the shape of the die, it was biased in favor of rolling a 3. We do not know the amount of bias. She experimented to estimate how likely it was for a 3 to be rolled and her results are in the above table.Using her experimental results find the best estimate of the probability of rolling a 3.

Solution

J u l ia ma d e a d i e f or a g am e . I t ha d 5 f a ces, l ab e l e d 1 - 5. B ec a u se o f t h e s ha p e o f t h e d i e, i t w a s bia se d in f a v or o f ro ll in g a 3. W e d o n o t kn o w t h e am o u n t o f bia s . S h e e x p er im e n t e d t o es t ima t e h o w l ik e l y i t w a s f or a 3 t o b e ro ll e d an d h er res u lt s a re in t h e ab o v e t ab l e . U s in g h er e x p er im e n t a l res u lt s f in d t h e b es t es t ima t e o f t h e p ro babi l i t y o f ro ll in g a 3.

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

The possible outcomes when \mathrm{a die is rolled} is

{1, 2, 3, 4, 5, 6} .

Therefore, the number of possible outcomes:

6

The number of favorable outcomes of \mathrm{rolling a 3}:

1

Probability

= \frac{number of favorable outcomes}{total number of outcomes}

= \frac{1}{6}