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23 March, 08:28

All the cars in the lot of a particular dealership have either a manual transmission or an automatic transmission, and all have either two doors or four doors. In this lot, 60% of the cars have a manual transmission and 70% of the cars have four doors. If 90% of the cars in the lot have either a manual transmission or four doors or both, then what percentage of the automatic transmission cars have four doors?

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  1. 23 March, 10:51
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    30%

    Step-by-step explanation:

    60% of the cars have manual transmission. This means P (Manual) = 60%

    70% of the cars have four doors. This means P (Four Doors) = 70%

    90% of the cars have either manual transmission or four doors or both. This means: P (Manual OR Four doors) = 90%

    The formula of probability in case of OR (Union) of two events A and B is:

    P (A or B) = P (A) + P (B) - P (A and B)

    Re-writing the formula for our case, we get:

    P (Manual or Four Doors) = P (Manual) + P (Four doors) - P (Both Manual and Four Doors)

    Using the given values, we get:

    90% = 60% + 70% - P (Both Manual and Four Doors)

    90% = 130% - P (Both Manual and Four Doors)

    P (Both Manual and Four Doors) = 130% - 90%

    P (Both Manual and Four Doors) = 40%

    This means, 40% vehicles have both Manual Transmission and Four Doors.

    Since, in total 70% of the cars have 4 doors, out of these 40% are manual. This means, the remaining 30% of the cars with 4 doors have automatic transmission.

    Hence, 30% of the automatic transmission cars have four doors
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