Question

2. A survey was given asking the following question “Have you ever been offended by something on social media? The table shows the response give. Using the table below answer the following questions.

Gender	Yes	No	Total
Female	625	541	1166
Male	685	510	1195
Total	1310	1051	2361

Suppose a person is chosen at random from this sample. Show your work by giving the fraction (using the numbers in the table above).   Either round your answers to 4 decimal places or give the fraction reduced to lowest terms.

1. Find the probability that the person is female.

2. Find the probability that the person was offended by something on social media.
   

3. Find the probability that a person was offended, given that the person is female.

4. Find the probability that the person is male, given that the person was not offended.
   
   

5. For this sample, are the events “being offended” and “being male” independent?   Explain your answer by using probabilities.

6. Find the probability of being offended and female.  

7. Find the probability of being offended or female.
   

8. Are the events “female” and “being offended” mutually exclusive? Why or why not?

Answer 1

a) P(female) = 1166 / 2361 = 0.4939

b) P(offended) = 1310 / 2361 = 0.5548

c) P(offended | female) = 625 / 1166 = 0.5360

d) P(male | not offended) = 510 / 1051 = 0.4853

e) P(offended | male) = 685 / 1195 = 0.5732

They are not independent events, because P(offended | male) ≠ P(offended)

f) P(offended and female) = 625 / 2361 = 0.2647

g) P(offended or female) = P(offended) + P(female) - P(offended and female)

                                        = 1310/2361 + 1166/2361 - 625/2361

                                        = 0.7840

h) No, they are not mutually exclusive events. Because P(offended and female) ≠ 0