Question 329566: on a basket of 50 oranges 8 are rotten. What is the probability of picking 2 rotten if 4 are picked from the basket?
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! A couple of ways to do this
let R =event of picking a rotten orange, G=the event of picking a good orange
1. You want RRGG but there are 4C2 ways to get to RR out of a sample of 4.
Each time you select without replacement the number available dwindles by one.
P(2 rotten out of 4) = 4C2RRGG = 6* 8/50*7/49*42*48*41/47 =0.105
2. The ways to select 2 rotten = 8C2=28, ways to select 2 good ones 42C2=861
The ways to select 4 oranges out of 50 = 50C4=230,300
P(2 rotten out of 4) = 8C2*42C2/50C4= 28*861/230300=0.105
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