Question 287482
A committee of 5 people is to be selected from student council. Council has 6 boys and 7 girls. What is the probability that the committee will have at least 3 boys? 

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The other tutor's solution is wrong.

We get the probability of the complement event
and subtract from 1.  The complement event is a committee with
no boys or 1 boy or 2 boys.

1 - P(0 boys OR 1 boy OR 2 boys)

"OR" means "ADD"

1 - [P(0 boys)+P(1 boy)+P(2 boys)]

P(0 boys) = P(5 girls) = {{{(7C5)/(13C5)=21/1287=7/429}}}

P(1 boy) =  P(4 girls AND 1 boy) 

"AND" means "MULTIPLY", so

P(1 boy) =  P(4 girls AND 1 boy) = {{{((7C4)(6C1))/(13C5)=((35)(6))/1287=210/1287=70/429}}}

P(2 boys) =  P(3 girls AND 2 boys) = {{{((7C3)(6C2))/(13C5)=((35)(15))/1287=525/1287=175/429}}}

So,

1 - [P(0 boys)+P(1 boy)+P(2 boys)]

becomes:

1 - [{{{7/429+70/428+175/429}}}]={{{1-252/429=429/429-252/429=177/429=59/143}}}

Edwin</pre>