jovic1104 wrote:

Hello to all Experts in Statistics/Probabilities

Please help me to solve the 2 probabilities questions below.

Q1. Three men are seeking for public office. Candidate A and B are given about the same chance of winning but Candidate C is given the chance twice as either A or B. What is the probability that A does not win? What is the probability of B?

Q2. In a certain children school, a teacher randomly selects 5 pre-schoolers from a class consisting of 10 boys and 5 girls. What is the probability of getting all 5 girls? 5 boys? Four boys and 1 girl?

It will be great if detailed explanation to the solution is provided. Many thanks in advance.

Q1. Three men are seeking for public office. Candidate A and B are given about the same chance of winning but Candidate C is given the chance twice as either A or B. What is the probability that A does not win? What is the probability of B?As there are only 3 candidates and assuming that either one of them must win, then their chances of winning must add up to 100%. So if chances of winning of A is

x%, then chances of winning of B will also be

x% and of C

2x%. Hence

x+x+2x=100% -->

x=25%=\frac{1}{4}.

So chances of B winning is

x=\frac{1}{4}Now, if chances of A winning is

\frac{1}{4}, then chances of

not winning will be

1-\frac{1}{4}=\frac{3}{4}.

Q2. In a certain children school, a teacher randomly selects 5 pre-schoolers from a class consisting of 10 boys and 5 girls. What is the probability of getting all 5 girls? 5 boys? Four boys and 1 girl?Probability=\frac{# \ of \ favorable \ outcomes}{total \ # \ of \ outcomes}A.

\frac{C^5_5}{C^5_{15}}, where

C^5_5 is the # of ways to choose 5 girls out of 5 and

C^5_{15} is the total # of ways to choose any 5 children out of total 15.

B.

\frac{C^5_{10}}{C^5_{15}}, where

C^5_{10} is the # of ways to choose 5 boys out of 5 and

C^5_{15} is the total # of ways to choose any 5 children out of 15.

C.

\frac{C^4_{10}*C^1_{5}}{C^5_{15}}, where

C^4_{10} is the # of ways to choose 4 boys out of 5,

C^1_5 is the # of ways to choose 1 girls out of 5 and

C^5_{15} is the total # of ways to choose any 5 children out of 15.

Hope it helps.

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