Question

A contingency table for injuries in the United States by circumstance (column variable) and gender (row variable) is given as follows. Note that frequencies are in millions.

		Circumstance
		Work (C1)	Home (C2)	Others (C3)	Total
Gender	Male (R1)	8.0	9.8	17.8	?
	Female (R2)	1.3	?	12.9	25.8
	Total	9.3	?	30.7	61.4

1. Complete the contingency table.

2. Find the probability that an injured person was hurt at work, that is, P(C1).

3. Find the probability that an injured person was hurt at work and she was a female, that is, P(C1 & R2).

4. Find the probability that a female injured person was hurt at work, that is, P(C1|R2).

5. Are events C1 and R2 independent? Explain your answer.

6. Are events C1and R2 mutually exclusive? Explain your answer.

7. Is the event that an injured person is male independent of the event that an injured person was hurt at home? Explain by calculation.

Answer 1

1)

	C1	C2	C3	total
R1	8	9.8	17.8	35.6
R2	1.3	11.6	12.9	25.8
total	9.3	21.4	30.7	61.4

2)

P(C1) =9.3/61.4 = 0.1515

3)

P(C1 and R2) =1.3/61.4 =0.0212

4)

P(C1| R2) =1.3/25.8 =0.0504

5)

no since P(C!) is not equal to P(C1 |R2)  C1 and R2 are not independent

6)no since there are 1.3 common elements between C1 and R2

7)

since P(R1)*P(C2) =(35.6/61.4)*(21.4/61.4)=0.2021 is not equal to P(R1 n C2) =9.8/61.4 =0.1596

events injured person is male is not independent of the event that an injured person was hurt at home