anonymous
  • anonymous
Jesse has eight friends who have volunteered to help with a school fundraiser. Five are boys and three are girls. If he randomly selects 3 friends to help him, find each probability? Probability of all boys or all girls
Algebra
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SOLVED
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chestercat
  • chestercat
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kropot72
  • kropot72
The probability of choosing a boy on the first selection is 5/8. Having chosen a boy on the first selection, there are 4 boys out of a total of 7 friends remaining. Therefore the probability of choosing a boy on the second selection is 4/7. Having chosen boys on the first and second selections, there are 3 boys out of a total of 6 friends remaining. Therefore the probability of choosing a boy on the third selection is 3/6. \[\large P(all\ boys)=\frac{5\times4\times3}{8\times7\times6}=you\ can\ calculate\]
anonymous
  • anonymous
Okay since the question is asking for all boys or all girls Do I do the same for the girls and add them together
kropot72
  • kropot72
The events 'all boys' and 'all girls' are mutually exclusive, therefore you need to calculate the probability of all girls (using the same reasoning as for all boys) and add the two values of probability.

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anonymous
  • anonymous
I got it It is 11/56 I have another question involving this problem it is asking for probability of at least 2 girls
kropot72
  • kropot72
You need to find the probability of exactly 2 girls. Then add that probability to the probability of all girls.
anonymous
  • anonymous
So 2 out of 8 + 3/8 Is 5/8
kropot72
  • kropot72
Not so. The probability of all girls is given by \[\large P(all\ girls)=\frac{3\times2\times1}{8\times7\times6}=you\ can\ calculate\] The probability of exactly 2 girls is given by \[\large P(2\ girls)=\frac{3C2\times5C1}{8C3}=\frac{3\times5}{56}=you\ can\ calculate\]
anonymous
  • anonymous
Okay so 1/56 plus 15/56 Is 16/56 simified is 4/14
kropot72
  • kropot72
And 4/14 simplified is 2/7.
anonymous
  • anonymous
I have one more Probability of at least 1 boy It's exact of 1 boy plus Al Boys correct So 1/56 plus what?
kropot72
  • kropot72
The probability of no boys is 1/56. Therefore the probability of at least 1 boy is given by \[\large P(at\ least\ 1\ boy)=1-1/56=you\ can\ calculate\]
anonymous
  • anonymous
So 0/56? But my book says it 55/56
kropot72
  • kropot72
How did you get 0/56? 1 - 1/56 = 55/56
anonymous
  • anonymous
Oh my bad I didn't do it correct Thank for helping me I appreciate it
kropot72
  • kropot72
You're welcome :)

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