Question

One hundred people were asked, "Do you favor stronger laws on gun control?" Of the 33 that answered "yes" to the question, 14 were male. Of the 67 that answered "no" to the question, six were male. If one person is selected at random,

1. What is the probability that this person answered "yes" or was a male? Round to 3 decimals (0.xxx)

2. What is the probability that this person answered "no" if they were a female? Round to 3 decimals (0.xxx)

Answer 1

To find the probabilities, we need to calculate the following:

1. The probability that a person answered "yes" or was a male:

- Number of people who answered "yes": 33

- Number of males who answered "yes": 14

- Total number of people: 100

P(answered "yes" or was a male) = (33 + 14) / 100

2. The probability that a person answered "no" if they were a female:

- Number of people who answered "no": 67

- Number of females who answered "no": 67 - 6 (since we know 6 males answered "no")

- Total number of females: 100 - 14 (since we know 14 males answered "yes")

P(answered "no" | female) = (67 - 6) / (100 - 14)

Calculating these probabilities:

1. P(answered "yes" or was a male) = (33 + 14) / 100 = 0.470

2. P(answered "no" | female) = (67 - 6) / (100 - 14) = 0.656

Therefore, the probability that a person selected at random answered "yes" or was a male is approximately 0.470, rounded to 3 decimals. The probability that a person selected at random, who is female, answered "no" is approximately 0.656, rounded to 3 decimals.