Question

section 5.1 homework
score: 4/17 answered: 4/17
question 5
a die is rolled. find the probability of the given event. round all answers to 4 decimals.
(a) the number showing is a 5;
the probability is :
(b) the number showing is an even number;
the probability is :
(c) the number showing is greater than 4;
the probability is :

Explanation:

Step1: Recall probability formula

The probability formula is $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in the event $E$ and $n(S)$ is the number of elements in the sample - space. When rolling a die, $n(S) = 6$ (the possible outcomes are 1, 2, 3, 4, 5, 6).

Step2: Calculate probability for (a)

For the event that the number showing is a 5, $n(E)=1$. So $P(5)=\frac{1}{6}\approx0.1667$.

Step3: Calculate probability for (b)

The even - numbered outcomes are 2, 4, 6. So $n(E) = 3$. Then $P(\text{even})=\frac{3}{6}=0.5000$.

Step4: Calculate probability for (c)

The numbers greater than 4 are 5 and 6. So $n(E)=2$. Then $P(\text{> 4})=\frac{2}{6}\approx0.3333$.

Answer:

(a) 0.1667
(b) 0.5000
(c) 0.3333