[9 minutes]
An election was held to choose the leader of a political party.

Candidate received of all the votes, and of s votes were cast by males.

Candidate received of all the votes, and of s votes were cast by males.

Candidate received of all the votes, and of s votes were cast by males.
A person , who voted in the election, is selected at random. Find the probability that
(i) voted for and is male,
(ii) is female,
(iii) voted for , given that is male.

Ask by Perkins Boone. in Singapore

Mar 13,2025

Question

[9 minutes]
An election was held to choose the leader of a political party.

Candidate received of all the votes, and of s votes were cast by males.

Candidate received of all the votes, and of s votes were cast by males.

Candidate received of all the votes, and of s votes were cast by males.
A person , who voted in the election, is selected at random. Find the probability that
(i) voted for and is male,
(ii) is female,
(iii) voted for , given that is male.

Ask by Perkins Boone. in Singapore

Mar 13,2025

UpStudy AI · Accepted Answer

**(i)**  
The probability that $$ V $$ voted for $$ A $$ is $$ 50\% $$ or $$ 0.5 $$. Since $$ 60\% $$ of $$ A $$'s votes were cast by males, the probability that $$ V $$ voted for $$ A $$ and is male is  
$$
P(A \text{ and male}) = 0.5 \times 0.6 = 0.3.
$$

**(ii)**  
First, compute the overall probability that a randomly selected voter is male by considering all candidates.  
- For candidate $$ A $$:  
  $$
  P(A \text{ and male}) = 0.5 \times 0.6 = 0.3.
  $$
- For candidate $$ B $$:  
  $$
  P(B \text{ and male}) = 0.35 \times 0.4 = 0.14.
  $$
- For candidate $$ C $$:  
  $$
  P(C \text{ and male}) = 0.15 \times 0.2 = 0.03.
  $$

The total probability that $$ V $$ is male is  
$$
P(\text{male}) = 0.3 + 0.14 + 0.03 = 0.47.
$$

Thus, the probability that $$ V $$ is female is  
$$
P(\text{female}) = 1 - P(\text{male}) = 1 - 0.47 = 0.53.
$$

**(iii)**  
We are to find the probability that $$ V $$ voted for $$ C $$, given that $$ V $$ is male. Using the conditional probability formula:  
$$
P(C \mid \text{male}) = \frac{P(C \text{ and male})}{P(\text{male})}.
$$
We already computed  
$$
P(C \text{ and male}) = 0.03 \quad \text{and} \quad P(\text{male}) = 0.47.
$$
Thus,  
$$
P(C \mid \text{male}) = \frac{0.03}{0.47} \approx 0.0638.
$$
**(i)** The probability that $$ V $$ voted for $$ A $$ and is male is $$ 30\% $$. **(ii)** The probability that $$ V $$ is female is $$ 53\% $$. **(iii)** The probability that $$ V $$ voted for $$ C $$ given that $$ V $$ is male is approximately $$ 6.38\% $$.

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