Question

Use the following information to answer the next six exercises. There are $23$countries in North America, $12$countries in

South America, $47$countries in Europe, $44$countries in Asia, $54$countries in Africa, and $14$in Oceania (Pacific Ocean

region).

Let A = the event that a country is in Asia.

Let E = the event that a country is in Europe.

Let F = the event that a country is in Africa.

Let N = the event that a country is in North America.

Let O = the event that a country is in Oceania.

Let S = the event that a country is in South America.

Find P(F).

Short answer

The solution is$$\begin{gathered} P\left(F\right)=\frac{54}{194} \\ =\frac{27}{97} \\ =0.28 \end{gathered}$$

Step-by-step solution

Given

Weareprovidedthefollowinginformationinthegivenquestion:

North America has 23 nations, South America has 12, Europe has 47 countries, Asia has 44 countries, Africa has 54 countries, and Oceania has 14 countries.

Concept used

Probabilityisametricfordetermininghowcertainweareoftheresultsofacertainexperiment.

Theprobabilityiscalculatedusingthefollowingformula:

Probability

$=\frac{\text{Fanorable number of cases}}{\text{Total number of cases}}$

If we flip a coin twice, the sample space associated with this random experiment is H H, H T, T H, T T, where T= tails and H= heads.

Let's say A= only has one tail.

Because localid="1648042601421" $$\begin{gathered} P\left(A\right)=\frac{2}{4} \\ =0.5 \end{gathered}$$, there are two outcomes that favor the event A H T, T H.

Calculation

Let A= the event that a country is in Asia.

Let E= the event that a country is in Europe.

Let F= the event that a country is in Africa.

Let N= the event that a country is in North America.

Let O= the event that a country is in Oceania.

Let S= the event that a country is in South America.

Now to find the probability that a country is in Africa, the favorable number of cases is 54 and total cases are $194$. Therefore, the probability that a country is in Africa is:

localid="1648042627718" $$\begin{gathered} P\left(F\right)=\frac{54}{194} \\ =0.28 \end{gathered}$$