Question

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

Answer 1

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.
\[\large P(all\ boys)=\frac{5\times4\times3}{8\times7\times6}=you\ can\ calculate\]

Answer 2

Okay since the question is asking for all boys or all girls
Do I do the same for the girls and add them together

Answer 3

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.

Answer 4

I got it
It is 11/56
I have another question involving this problem it is asking for probability of at least 2 girls

Answer 5

You need to find the probability of exactly 2 girls. Then add that probability to the probability of all girls.

Answer 6

So
2 out of 8 + 3/8
Is 5/8

Answer 7

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
\[\large P(2\ girls)=\frac{3C2\times5C1}{8C3}=\frac{3\times5}{56}=you\ can\ calculate\]

Answer 8

Okay so 1/56 plus 15/56
Is 16/56 simified is 4/14

Answer 9

And 4/14 simplified is 2/7.

Answer 10

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?

Answer 11

The probability of no boys is 1/56. Therefore the probability of at least 1 boy is given by
\[\large P(at\ least\ 1\ boy)=1-1/56=you\ can\ calculate\]

Answer 12

So 0/56?
But my book says it 55/56

Answer 13

How did you get 0/56?
1 - 1/56 = 55/56

Answer 14

Oh my bad I didn't do it correct
Thank for helping me I appreciate it

Answer 15

You're welcome :)