The contingency table below displays the results of a study investigating the effectiveness of bicycle helmets in preventing head injury (1989). The data consist of a random sample of 793 individuals who were involved in bicycle accidents during a particular one-year interval.
wearing
helmet
Y
N
totals
head
injury
Y
17
218
235
N
130
428
558
totals
147
646
793
For instance, of the 793 individuals involved in bicycle accidents, 147 were wearing safety helmets, and 646 were not. Among those wearing helmets, 17 suffered head injuries requiring the attention of a doctor, and 130 did not.
Calculate the probability that a randomly chosen person (in the group of 793) suffered a head injury. [ P(HI) ] [2 marks]
Calculate the probability that a randomly chosen person (in the group of 793) was wearing a safety helmet. [ P(SH) ] [2 marks]
Explain what is wrong with the following. The probability that a person was wearing a safety helmet or suffered a head injury is P(SH) + P(HI). [2 marks]
Calculate the probability that a random person from the group of 793 was wearing a safety helmet or suffered a head injury. [2 marks]