Question

You roll a six-sided die and observe the number showing on the top side when the die comes to rest. What is the probability of observing:a. an even number? b. a number greater than 0? c. a number less than 4? d. a prime number?

Answer 1

For all the questions we will use the following quotient to determine the probability that an event occurs:

$\frac{\text{Favorable cases}}{Total\text{ cases}}.$

For all the questions the number of total cases is 6.

For the first question, we count the number of even numbers of a die: 2, 4, and 6.

For the second question, we count the number of numbers greater than 0: 1, 2, 3, 4, 5, and 6.

For the third question, we count the number of numbers less than 4: 1, 2, and 3.

For the last question, we count the number of prime numbers between 1 and 6: 2, 3, and 5.

Answer:

(a)

$\frac{3}{6}=0.5.$

(b)

$\frac{6}{6}=1.$

(c)

$\frac{3}{6}=0.5.$

(d)

$\frac{3}{6}=0.5.$