A survey of 200 downtown workers revealed that 31 females ride the train, 24 females ride the
bus and 35 females car pool. The survey also found that 44 males ride the train, 38 males ride
the bus and 28 males car pool.

Male

Female
 
Train

44

31

75

Bus

38

24

62

Car Pool

28

35

63

110

90

200

What is the probability that a randomly selected person is male or is car pooling?

To find the probability that a randomly selected person is male or is carpooling, we use the principle of inclusion and exclusion in probability. The formula for this is:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

Where:
- \( A \) is the event that the person is male.
- \( B \) is the event that the person is carpooling.

### Step 1: Calculate \( P(A) \)

The probability that a person is male:
\[
P(A) = \frac{\text{Number of males}}{\text{Total number of people}} = \frac{110}{200} = 0.55
\]

### Step 2: Calculate \( P(B) \)

The probability that a person is carpooling:
\[
P(B) = \frac{\text{Number of people carpooling}}{\text{Total number of people}} = \frac{63}{200} = 0.315
\]

### Step 3: Calculate \( P(A \cap B) \)

The probability that a person is both male and carpooling:
\[
P(A \cap B) = \frac{\text{Number of males carpooling}}{\text{Total number of people}} = \frac{28}{200} = 0.14
\]

### Step 4: Calculate \( P(A \cup B) \)

Using the principle of inclusion and exclusion:
\[
P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.55 + 0.315 - 0.14 = 0.725
\]

Therefore, the probability that a randomly selected person is male or is carpooling is 0.725 or 72.5%.

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Do you want more details or have any questions?

Here are some related questions:

1. What is the probability that a randomly selected person is female or rides the bus?
2. What is the probability that a randomly selected person is male and rides the train?
3. What is the probability that a randomly selected person is female or rides the train?
4. What is the probability that a randomly selected person rides the bus or carpools?
5. What is the probability that a randomly selected person is female and rides the bus?
6. What is the probability that a randomly selected person is male and does not carpool?
7. What is the probability that a randomly selected person is female and does not ride the train?
8. What is the probability that a randomly selected person rides the train and carpools?

**Tip:** When solving probability problems involving "or" conditions, always remember to subtract the overlap (the intersection of the two events) to avoid double counting.

Explore the probability that a randomly selected person is male or carpooling using the principle of inclusion and exclusion. Includes step-by-step calculations and explanations based on survey data of 200 downtown workers.

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