Question

In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Russian Presidential Election. According to the Central Election Commission of the Russian Federation, a frequency distribution for the March 4. 2012 Russian presidential election is as follows.

Find the probability that a randomly selected voter voted for

a. Putin.

b. either Zhirinovsky or Mironov.

c. someone other than Putin.

Short answer

Find the probability that a randomly selected voter voted for

(a) 0.644.

(b). 0.102.

(c). 0.356.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

According to the Central Election Commission of the Russian Federation, a frequency distribution for the March 4. 2012 Russian presidential election is as follows:

Candidate	Votes
Vladimir Putin	45,513,001
Gennady Zyuganov	12,288,624
Mikhail Prokhorov	5,680,558
Vladimir Zhirinovsky	4,448,959
Sergey Mironov	2,755,642

Part (a) Step 2. Find the probability that a randomly selected voter voted for Putin.

We know that an event's probability ranges from 0 to 1, and both 0 and 1 are included in it.

The formula for the probability of an event is:

$P\left(E\right)=\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$

A total of 70,686,784 votes were voted in the Russian Presidential Election. Therefore, the total number of instances will become 70,686,784.

The total instances where a voter voted for Putin is:

45,513,001

Let's call the occurrence 'E' where a voter voted for Putin.

The probability that a voter voted for Putin is:

$$\begin{gathered} P\left(E\right)=\frac{45,513,001}{70,686,784} \\ =0.644 \end{gathered}$$

Part (b) Step 1. Find the probability that a randomly selected voter voted for either Zhirinovsky or Mironov.

The total instances where a voter voted for either Zhirinovsky or Mironov is:

$4,448,959+2,755,642=7,204,601$

Let's call the occurrence 'E' where a voter voted for either Zhirinovsky or Mironov.

The probability that a voter voted for either Zhirinovsky or Mironov is:

$$\begin{gathered} P\left(E\right)=\frac{7,204,601}{70,686,784} \\ =0.102 \end{gathered}$$

Part (c) Step 1. Find the probability that a randomly selected voter voted for someone other than Putin.

The total instances where a voter voted for someone other than Putin are:

$12,288,624+5,680,5584,448,959+2,755,642=25,173,798$

Let's call the occurrence 'E' where a voter voted for someone other than Putin.

The probability that a voter voted for someone other than Putin is:

$$\begin{gathered} P\left(E\right)=\frac{25,173,798}{70,686,784} \\ =0.356 \end{gathered}$$