Answer:
Follows are the solution to this question:
Step-by-step explanation:
![Frequency\ total = 155 + 256 + 144 + 145 = 700;](https://tex.z-dn.net/?f=Frequency%5C%20%20total%20%3D%20155%20%2B%20256%20%2B%20144%20%2B%20145%20%3D%20700%3B)
In point (1):
Now that it is possible to obtain the joint distribution as:
![IT\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ G \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Total](https://tex.z-dn.net/?f=IT%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%09G%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%09Total)
![Yes \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{155}{700} = 0.2214\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{256}{700} = 0.3657 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.5871\\\\No \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{145}{700} = 0.2071\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{144}{700} = 0.2057\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.4128\\\\Total \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.4285 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.5714\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1](https://tex.z-dn.net/?f=Yes%09%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5Cfrac%7B155%7D%7B700%7D%20%3D%200.2214%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%09%5Cfrac%7B256%7D%7B700%7D%20%3D%200.3657%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%090.5871%5C%5C%5C%5CNo%09%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5Cfrac%7B145%7D%7B700%7D%20%3D%200.2071%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%09%5Cfrac%7B144%7D%7B700%7D%20%3D%200.2057%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%090.4128%5C%5C%5C%5CTotal%09%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%200.4285%09%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%200.5714%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%09%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%201)
In point (2):
Likely that now It (the IT column total throughout the table above) seems to be the random individual selected = 0.4285;
Here, 0.4285 is the necessary probability.
In point (3):
The way of its worker's sleep at work =0.5871 ( first row total in the above table )
Here 0.5871 was its required probability.
In point (4):
In this as employee slept at work, he is likely to also be from IT to be calculated with:
![=\frac{\text{probability he was just an IT-former but was asleep at work}}{ \text{possibly he worked at work}}\\\\=\frac{0.2214}{0.5871} \\\\ =0.3771 \text{was its probability required here}.](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7Bprobability%20he%20was%20just%20an%20IT-former%20but%20was%20asleep%20at%20work%7D%7D%7B%20%5Ctext%7Bpossibly%20he%20worked%20at%20work%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B0.2214%7D%7B0.5871%7D%20%5C%5C%5C%5C%20%3D0.3771%20%20%5Ctext%7Bwas%20its%20probability%20required%20here%7D.)
In point (5):
In an individual is also an official government, its chance of getting sleep at work is measured when:
![= \frac{\text{Probability he is professional in business slept at work}}{\text{or that he is officially in business}} \\\\= \frac{0.3657}{0.5714}\\\\ = 0.6400 \text{is the required probability here}.](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%5Ctext%7BProbability%20he%20is%20professional%20in%20business%20slept%20at%20work%7D%7D%7B%5Ctext%7Bor%20that%20he%20is%20officially%20in%20business%7D%7D%20%5C%5C%5C%5C%3D%20%5Cfrac%7B0.3657%7D%7B0.5714%7D%5C%5C%5C%5C%20%3D%200.6400%20%5Ctext%7Bis%20the%20required%20probability%20here%7D.)
In point (6):
![\to P(IT) \ P(Yes) = 0.4285 \times 0.5871 = 0.2516 \\\\\to P(IT and Yes ) = 0.2214 \\\\](https://tex.z-dn.net/?f=%5Cto%20P%28IT%29%20%5C%20P%28Yes%29%20%3D%200.4285%20%5Ctimes%200.5871%20%3D%200.2516%20%5C%5C%5C%5C%5Cto%20P%28IT%20and%20Yes%20%29%20%3D%200.2214%20%5C%5C%5C%5C)
Therefore, 2 cases aren't independent, because P(IT) P(Yes) is not the same as P(IT and Yes), which also implies that P(IT|Yes) is not the same as P (IT), therefore "
" is correct.