USING YOUR MATH A standard die is rolled a single time and the number of dots on the upward facing side is noted. List the outcomes in the sample space for throwing the die just once. Given the event of rolling a number less than 5 , list all the outcomes from (a) that fall into this event. What is the probability of rolling number less than 5

Solution

U S I NG Y O U R M A T H A s t an d a r d d i e i s ro ll e d a s in g l e t im e an d t h e n u mb er o f d o t s o n t h e u pw a r d f a c in g s i d e i s n o t e d . L i s t t h e o u t co m es in t h e s am pl e s p a ce f or t h ro w in g t h e d i e j u s t o n ce . G i v e n t h e e v e n t o f ro ll in g a n u mb er l ess t han 5, l i s t a ll t h e o u t co m es f ro m (a) t ha t f a ll in t o t hi s e v e n t . Wha t i s t h e p ro babi l i t y o f ro ll in g n u mb er l ess t han 5

\frac{2}{3}

Decimal

0.66666 \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 number less than 5}:

4

Probability

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

= \frac{4}{6}

Cancel the common factor:

2

= \frac{2}{3}