# 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 ^{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?

**Answer:**

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+**)?

**Answer:**

P (Blood type O) = 49%

P (Rhesus Factor present) = 85%

P (Blood type O+) = ^{49}⁄_{100} × ^{85}⁄_{100} = 0.4165 or 41.65%