Question

a die is rolled. find the probability of the given event.
write your answers as whole numbers or reduced fractions.
(a) the number showing is a 2
$p(2) =$
(b) the number showing is an even number
$p(even) =$
(c) the number showing is greater than 5
$p(greater than 5) =$

Explanation:

Step1: Determine the total number of outcomes

When a die is rolled, there are \(n = 6\) possible outcomes (\(1,2,3,4,5,6\)).

Step2: Calculate \(P(2)\)

The event of getting a \(2\) has \(m_1=1\) favorable outcome. Using the probability formula \(P=\frac{m}{n}\), we have \(P(2)=\frac{1}{6}\).

Step3: Calculate \(P(\text{even})\)

The even - numbered outcomes are \(2,4,6\), so \(m_2 = 3\). Then \(P(\text{even})=\frac{3}{6}=\frac{1}{2}\).

Step4: Calculate \(P(\text{greater than }5)\)

The number greater than \(5\) on a die is \(6\), so \(m_3=1\). Then \(P(\text{greater than }5)=\frac{1}{6}\).

Answer:

(a) \(\frac{1}{6}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{1}{6}\)