Of the 64 people who answered "yes" to a question, 6 were male. Of the 70 people that answered "no" to the question, 8 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?

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To find the probability that a person answered "yes" or was male, we need to calculate the total number of people who answered "yes" or were male, and divide it by the total number of people in the group.

Step 1: Calculate the number of people who answered "yes".
From the given information, we know that there were 64 people who answered "yes".

Step 2: Calculate the number of people who were male.
From the given information, we know that there were 6 males who answered "yes" and 8 males who answered "no". Therefore, the total number of males is 6 + 8 = 14.

Step 3: Calculate the total number of people in the group.
To calculate the total number of people in the group, we sum the number of people who answered "yes" and the number of people who answered "no". So, the total number of people in the group is 64 + 70 = 134.

Step 4: Calculate the probability.
The probability that a person answered "yes" or was male is equal to the sum of the number of people who answered "yes" and the number of males, divided by the total number of people in the group. So, the probability is (64 + 14) / 134.

Step 5: Simplify the expression to get the final answer.
The simplified form is 78 / 134.

Therefore, the probability that a person selected at random from the group answered "yes" or was male is 78/134, which can also be written as approximately 0.582.

To find the probability that the person answered "yes" or was male, we need to calculate the probability of each event individually and then subtract the probability of their intersection.

First, let's calculate the probability of answering "yes". Out of the total number of people who answered the question, which is 64 + 70 = 134, the number of people who answered "yes" is 64. Therefore, the probability of answering "yes" is:

P(yes) = number of people who answered "yes" / total number of people who answered the question
= 64 / 134
= 0.4776 (rounded to four decimal places)

Next, let's calculate the probability of being male. Out of the total number of people, which is 64 + 70 = 134, the number of males is 6 + 8 = 14. Therefore, the probability of being male is:

P(male) = number of males / total number of people
= 14 / 134
= 0.1045 (rounded to four decimal places)

Now, let's calculate the probability of both answering "yes" and being male. From the given information, we know that 6 people were male and answered "yes". Therefore, the probability of both events occurring is:

P(yes and male) = number of males who answered "yes" / total number of people
= 6 / 134
= 0.0448 (rounded to four decimal places)

To find the probability of answering "yes" or being male, we add the probability of each event and subtract the probability of their intersection.

P(yes or male) = P(yes) + P(male) - P(yes and male)
= 0.4776 + 0.1045 - 0.0448
= 0.5373 (rounded to four decimal places)

Therefore, the probability that a randomly selected person answered "yes" or was male is approximately 0.5373.