Two-Stage Probability In Real Life
Before viewing this page, it would be helpful to first read Two-Stage Probability in Gambling.
Example One - Having Two Children
In a family with 2 children, what is the probability of having 2 sons?
This is the same as tossing 2 fair coins. The probability of having a baby boy is 1⁄2. The probability of having a baby girl is also 1⁄2.
P (2 boys) = 1⁄2 × 1⁄2 = 1⁄4
Example Two - Drink-Driving
According to the Queensland Police Service, there are 45 under-aged drivers for every 1000 drivers on the road. Also, it was found that 1% of drivers of all ages drink-drive. What is the probability that in a random roadside breath test, police will catch an under-age drink-driver?
P (under-aged drink-driver) = 1⁄100 × 45⁄1000 = 45⁄100000 = 0.00045
(The frightening part is that an intoxicated, inexperienced driver is driving a powerful, fast vehicle with no insurance on the same road as you and me!)
Question - Blood Types
There are 4 main blood types - A, B, AB and O. In addition to these, people may have the Rhesus Factor (an identifying chemical in blood) or not. If a person has the Rhesus Factor, the blood type is said to be positive and if another person doesn't have the Rhesus Factor, the blood type is said negative. For example, a person whose blood type is B and who also has Rhesus Factor is B+.
The percentage of the population with the 4 main blood types is: A 38%; B 7%; AB 3%; and O 49%.
The percentage of the population with the Rhesus Factor and therefore positive (+) is 85%.
What is the probability that a person will have a blood type O and the Rhesus factor (O+)?
P (Blood type O) = 49%
P (Rhesus Factor present) = 85%
P (Blood type O+) = 49⁄100 × 85⁄100 = 0.4165 or 41.65%