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?

Answer:

This is the same as tossing 2 fair coins. The probability of having a baby boy is 12. The probability of having a baby girl is also 12.

P (2 boys) = 12 × 12 = 14


Example Two - Drink-Driving

Car Crash

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?

Answer:
P (under-aged drink-driver) = 1100 × 451000 = 45100000 = 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

Blood Samples

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+)?

Answer:

P (Blood type O) = 49%
P (Rhesus Factor present) = 85%
P (Blood type O+) = 49100 × 85100 = 0.4165 or 41.65%