Answer:
i. [tex]P(A) = \frac{1}{10}[/tex]
ii. [tex]P(B) = \frac{1}{10}[/tex]
iii. [tex]P(A) = \frac{3}{5}[/tex]
iv. [tex]P(B) = \frac{2}{5}[/tex]
Step-by-step explanation:
Given
Time: 07 2(A) 5(B)
Calculating (a)
First, we need to list out the possible sample space, S of A
[tex]S = \{0,1,2,3,....,9\}[/tex]
[tex]n(S) = 10[/tex]
Probability of A being a 4 is the number of occurrence of 4 divided by the number of sample space
[tex]A = \{4\}[/tex]
[tex]n(A) = 1[/tex]
Hence;
[tex]P(A) = \frac{n(A)}{n(S)}[/tex]
[tex]P(A) = \frac{1}{10}[/tex]
Calculating (b)
First, we need to list out the possible sample space, S of B
[tex]S = \{0,1,2,3,....,9\}[/tex]
[tex]n(S) = 10[/tex]
Probability of B being a 8 is the number of occurrence of 8 divided by the number of sample space
[tex]B = \{8\}[/tex]
[tex]n(B) = 1[/tex]
Hence;
[tex]P(B) = \frac{n(B)}{n(S)}[/tex]
[tex]P(B) = \frac{1}{10}[/tex]
Calculating (c)
Using the sample space in (a)
[tex]n(S) = 10[/tex]
Probability of A being less than 6 is the number of occurrence of less than 6 divided by the number of sample space
[tex]A = \{0,1,2,3,4,5\}[/tex]
[tex]n(A) = 6[/tex]
Hence;
[tex]P(A) = \frac{n(A)}{n(S)}[/tex]
[tex]P(A) = \frac{6}{10}[/tex]
[tex]P(A) = \frac{3}{5}[/tex]
Calculating (d)
Using the sample space in (b)
[tex]n(S) = 10[/tex]
Probability of B being greater than 5 is the number of occurrence of greater than 5 divided by the number of sample space
[tex]B = \{6,7,8,9\}[/tex]
[tex]n(B) = 4[/tex]
Hence;
[tex]P(B) = \frac{n(B)}{n(S)}[/tex]
[tex]P(B) = \frac{4}{10}[/tex]
[tex]P(B) = \frac{2}{5}[/tex]
