Question

The table below shows information about people who visited a hospital with a broken bone and where the broken bone was.

One of the people was chosen at random. Work out the probability that the person was
a) an adult with a broken foot.
b) an adult, given that they had a broken foot.​

Answer 1

Total for adult is 15+7+3+20+5+8 =58

for broken foot = 7/58

b) 7/7+5 = 7/12

Answer 2

a) The probability of selecting an adult with a broken foot is 7/58. b) The probability of selecting an adult, given that they had a broken foot, is 7/12.

To determine the probability of randomly selecting a person with a specific condition from the hospital data, we can use the concept of conditional probability.

a) Probability of selecting an adult with a broken foot:

P(Adult and Broken Foot) = Number of Adults with Broken Foot / Total Number of People

P(Adult and Broken Foot) = 7 / (15 + 7 + 3 + 20 + 5 + 8)

P(Adult and Broken Foot) = 7 / 58

b) Probability of selecting an adult given they had a broken foot:

P(Adult | Broken Foot) = Number of Adults with Broken Foot / Total Number of People with Broken Foot

P(Adult | Broken Foot) = 7 / (7 + 5)

P(Adult | Broken Foot) = 7 / 12