One hundred employees of a company are asked how they get to work and whether they work full time or part time. The table below

One hundred employees of a company are asked how they get to work and whether they work full time or part time. The table below shows the results. If one of the 100 employees is randomly selected, find the probability that the person drives alone or bicycles to work.

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  1. The probability is 56/100, or 14/25 = 0.56.

    These events are not mutually exclusive, meaning they can happen at the same time.  This means we use

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

    P(carpool or full time) = P(carpool) + P(full time) - P(carpool & full time)

    There are 6+9=15 people out of 100 that carpool.
    There are 7+4+30+6=47 people out of 100 that work full time.
    There are 6 people out of 100 that carpool and work full time.

    This gives us
    15/100 + 47/100 - 6/100 = 56/100

  2. 0.67

    Step-by-step explanation:

    There are 3+4 = 7 people who bicycle to work.  There are 32+28 = 60 people who drive alone to work.  This makes 7+60 = 67 people.

    This makes the probability 67/100 = 0.67.

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