Question

Sources of Energy Use A breakdown of the sources of energy used in a country is shown below.Hydropower 3%Oil 42%Natural Gas 20%Coal 27%Nuclear 5%Other 3%(a) Not hydropowerP (Not hydropower) =(b) Oil or hydropowerP (Oil or hydropower) =(c) CoalP(Coal )=

Answer 1

First, we need to make sure that we have the percentages of all the possible sources of energy (check that the percentages add up to 100%).

$3+42+20+27+5+3=100$

Now, we can calculate the probabilities.

a)

$\begin{gathered} P(NotHydropower)=1-P(Hydropower)=1-3\text{percent}=1-0.03=0.97 \\ \Rightarrow P(NotHydropower)=0.97 \end{gathered}$

P(Not Hydropower)=0.97

b)

$\begin{gathered} P(OilOrHydropower)=P(Oil)+P(Hydropower)=0.42+0.03=0.45 \\ \Rightarrow P(OilOrHydropower)=0.45 \end{gathered}$

Notice that the two events are independent. P(Oil or Hydropower)=0.45.

c)

$\begin{gathered} P(coal)=27\text{percent}=0.27 \\ \Rightarrow P(coal)=0.27 \end{gathered}$

P(Coal)=0.27