SOLUTION: A hat contains 25 coins - 7 gold, 6 silver and 12 copper. We randomly select two coins from the hat without replacement. a) Let X be the number of gold coins selected. Find th

Question 1025545: A hat contains 25 coins - 7 gold, 6 silver and 12 copper. We randomly select two coins from the hat without replacement.
a) Let X be the number of gold coins selected. Find the probability distribution of X.
b) What is the probability that X = 1 if no silver coins are selected?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
General case:
first coin is
gold: 7/25, silver 6/25, copper 12/25.
second coin
if first gold, second coin is gold (6/24), silver (6/24), copper (12/24).
if first silver, second is gold (7/24), silver (5/24), copper (12/24)
if first copper, second is gold (7/24), silver (6/24) copper (11/24).
Make a tree diagram
GG=42/600
GS=42/600
GC=84/600
SG=42/600
SS=30/600
SC=72/600
CG=84/600
CS=72/600
CC=132/600
--------------------
Probability of 1 gold with no silver
GG=42/600NO
GS=42/600NO
GC=84/600YES
SG=42/600NO
SS=30/600NO
SC=72/600NO
CG=84/600YES
CS=72/600NO
CC=132/600NO
The probability is only GC or CG, and that is 168/600 or 7/25.
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