Question

11.2: probability
score: 7/16 answered: 5/10
question 4
a die is rolled. find the probability of the given event.
(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 2;
the probability is

Explanation:

Step1: Determine the total number of outcomes

When a die is rolled, the total number of possible outcomes is $n = 6$ (the numbers $1,2,3,4,5,6$).

Step2: Calculate probability for part (a)

For the event “the number showing is a $5$”, the number of favorable outcomes $m_1=1$.
Using the probability formula $P=\frac{m}{n}$, we have $P_1=\frac{1}{6}$.

Step3: Calculate probability for part (b)

For the event “the number showing is an even number” (the numbers $2,4,6$), the number of favorable outcomes $m_2 = 3$.
Using the probability formula $P=\frac{m}{n}$, we have $P_2=\frac{3}{6}=\frac{1}{2}$.

Step4: Calculate probability for part (c)

For the event “the number showing is greater than $2$” (the numbers $3,4,5,6$), the number of favorable outcomes $m_3=4$.
Using the probability formula $P=\frac{m}{n}$, we have $P_3=\frac{4}{6}=\frac{2}{3}$.

Answer:

a) $\frac{1}{6}$
b) $\frac{1}{2}$
c) $\frac{2}{3}$