Made Easy Full Syllabus Test 3 Probability

Question

can anyone verify if options are correct i am not satisfied with the solution given. 

Comments

$P_1 = 0.3 \times 0.8 + 0.7 \times 0.3 = 0.45$

$P_2 = \dfrac{0.7 \times 0.3}{0.7} = 0.3$ (This is infact directly given in the question sentence)

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Lets say:

1. We have 100 students.
2. 0.3 of them are requesting for GPU so we have 30 students requesting for GPU and the rest 70 students are not requesting for GPU.
3. The probability that a student requesting for a GPU is assigned a system with 12^th gen Intel CPU is 0.8, so we have 30 students requesting for GPU among which 0.8*30 = 24 students are assigned the system and the rest 6 students who are requesting are not assigned.
4. The probability that a student not requesting for a GPU is assigned a system with 12th gen Intel CPU is 0.3, so we have 70 students not requesting for GPU among which 0.3*70 = 21 students are assigned the system and the rest 49 students who are not requesting are not assigned.

$P_{1}$ = probability that a student gets assigned a system with 12^th gen Intel CPU = (24+21)/100 

      = 45/100.

$P_{2}$ = probability that a student get assigned a system wth 12^th gen Intel CPU given that he/she

         not request for a GPU

      = 21/70.

I am not getting any of the options.