Question 1085606: Use the multiplication rule for dependent events to solve for the following: A presenter needs two volunteers to help with an experiment. There are 30 total people to select from; 18 are women and 12 are men. He randomly chooses one volunteer who comes to the front of the room. He then chooses a second volunteer from those still seated. What is the probability that both volunteers chosen are women? Start with:
P(woman 1st and woman 2nd) =
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
Use the multiplication rule for dependent events to solve for the following: A presenter needs two volunteers to help with an experiment. There are 30 total people to select from; 18 are women and 12 are men. He randomly chooses one volunteer who comes to the front of the room. He then chooses a second volunteer from those still seated. What is the probability that both volunteers chosen are women? Start with:
P(woman 1st and woman 2nd) =
Solution:
Step 1:
From 18 women and 12 men,
P(woman)=18/30
Step 2:
From 17 women and 12 men,
P(woman)=17/29
Apply multiplication rule,
P(woman,woman)=18/30*17/29=51/145
Alternatively, apply hypergeometric distribution:
W=18
M=12
w=number of women chosen
m=number of men chosen
P(w,m)=C(W,w)*C(M,m)/C(W+M,w+m)
where
C(n,r)=combination of r chosen from n)=n!/(r!(n-r)!)
=>
P(2,0)=C(18,2)C(12,0)/C(30,2)
=51/145 as before.
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