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(1) Consider first statement of the problem:
Of the total fleet of 20 cars, 13 cars are 2-doors.
From this statement, 20-13 = 7 cars are 4-doors.
(2) Consider the second and the third statements:
of the 13 2-doors cars, 12 have automatic transmission (AT).
There are only 4 cars with manual transmission (MT).
From these two statements, one can make the following conclusions:
- Of the 13 2-doors cars, 1 has manual transmission;
- of the 7 4-doors cars, 3 have manual transmission and 4 have automatic transmission.
Let us ORGANISE this information.
There are 13 2-doors cars; of them, 12 have AT and 1 have MT.
7 4-doors cars; of them, 4 have AT and 3 have MT.
Now I am in the position to answer problem's questions.
(A) P = . ANSWER
(B) P = = = . ANSWER
Completed and solved.
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The key in solving this problem is to organize and to present the information in a compact and clear logical form.
To get it, you need to extract / (to deduce) all logical consequences from the given info.
Surely, it is assumed, that you firmly know this formula for the conditional probability
P( M | N ) = ,
where M and N are subsets of the universal set.