Find the indicated probability.
Of the 62 people who answered "yes" to a question, 11 were male. Of the 53 people that answered "no" to the question, 7 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?
0.696
0.177
0.157
0.6

We are asked to find the probability that a randomly selected person either answered "yes" to the question or is male. 

This is an application of the **union of two events**. The formula for the probability of the union of two events is:

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

Where:
- \(P(A)\) is the probability that a person answered "yes".
- \(P(B)\) is the probability that a person is male.
- \(P(A \cap B)\) is the probability that a person answered "yes" and is male (i.e., a male who answered "yes").

### Step 1: Total number of people
The total number of people in the group is:
\[
62 \text{ (answered "yes")} + 53 \text{ (answered "no")} = 115 \text{ people}.
\]

### Step 2: Probability that a person answered "yes" \(P(A)\)
The number of people who answered "yes" is 62. So, the probability that a randomly selected person answered "yes" is:
\[
P(A) = \frac{62}{115}.
\]

### Step 3: Probability that a person is male \(P(B)\)
The total number of males is \(11 \text{ (males who answered "yes")} + 7 \text{ (males who answered "no")}\), so:
\[
P(B) = \frac{11 + 7}{115} = \frac{18}{115}.
\]

### Step 4: Probability that a person is a male and answered "yes" \(P(A \cap B)\)
The number of males who answered "yes" is 11, so:
\[
P(A \cap B) = \frac{11}{115}.
\]

### Step 5: Apply the formula for the union of two events
Now we substitute the values into the formula:

\[
P(A \cup B) = \frac{62}{115} + \frac{18}{115} - \frac{11}{115}
\]
\[
P(A \cup B) = \frac{62 + 18 - 11}{115} = \frac{69}{115}.
\]

### Step 6: Simplify the result
\[
P(A \cup B) = 0.6.
\]

Thus, the probability that a randomly selected person answered "yes" or was male is **0.6**.

The correct answer is:
\[
\boxed{0.6}.
\]

Do you want more details or have any questions?

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**Related Questions:**
1. What is the probability that a randomly selected person answered "no"?
2. What is the probability that a randomly selected person is female?
3. How do we calculate the probability of the intersection of two events?
4. What is the complement rule in probability, and how can it be used here?
5. How do you interpret probabilities in real-world contexts?

**Tip:** When calculating probabilities for combined events, always remember to subtract the overlap (intersection) to avoid double-counting.

Find the indicated probability. Of the 62 people who answered "yes" to a question, 11 were male. Of the 53 people that answered "no" to the question, 7 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?

Learn how to calculate the probability that a randomly selected person answered "yes" or was male. This probability problem involves the union of two events and applies key probability concepts, with a step-by-step solution involving the formula for P(A ∪ B).

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