Answer:
a. [tex]\frac{1}{15}[/tex]
b. [tex]\frac{2}{5}[/tex]
c. [tex]\frac{14}{15}[/tex]
d. [tex]\frac{8}{15}[/tex]
Step-by-step explanation:
Given that there are two laptop machines and four desktop machines.
On a day, 2 computers to be set up.
To find:
a. probability that both selected setups are for laptop computers?
b. probability that both selected setups are desktop machines?
c. probability that at least one selected setup is for a desktop computer?
d. probability that at least one computer of each type is chosen for setup?
Solution:
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
a. Favorable cases for Both the laptops to be selected = [tex]_2C_2[/tex] = 1
Total number of cases = 15
Required probability is [tex]\frac{1}{15}[/tex].
b. Favorable cases for both the desktop machines selected = [tex]_4C_2=6[/tex]
Total number of cases = 15
Required probability is [tex]\frac{6}{15} = \frac{2}{5}[/tex].
c. At least one desktop:
Two cases:
1. 1 desktop and 1 laptop:
Favorable cases = [tex]_2C_1\times _4C_1 = 8[/tex]
2. Both desktop:
Favorable cases = [tex]_4C_2=6[/tex]
Total number of favorable cases = 8 + 6 = 14
Required probability is [tex]\frac{14}{15}[/tex].
d. 1 desktop and 1 laptop:
Favorable cases = [tex]_2C_1\times _4C_1 = 8[/tex]
Total number of cases = 15
Required probability is [tex]\frac{8}{15}[/tex].
