AXISHK
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Probability question
Nine coins of which three are gold and six are silver in a box. Three coins are selected and placed in bag A. The remaining coins are placed in bag B.
1. Find the probabilities of each possible numbers of gold coins, from 0 to 3, in bag A.
2. on a particular case it is know that one gold coin and two silver cons are in bag A, and that the remaining coins are in bag B. One coin is drawn from a bag selected randomly and put it into another bag. If one coin is then drawn from the last bag, find the probability that it is a gold coin.
1. Find the probabilities of each possible numbers of gold coins, from 0 to 3, in bag A.
2. on a particular case it is know that one gold coin and two silver cons are in bag A, and that the remaining coins are in bag B. One coin is drawn from a bag selected randomly and put it into another bag. If one coin is then drawn from the last bag, find the probability that it is a gold coin.
ASKER
"Find the probabilities of each possible numbers of gold coins, from 0 to 3, in bag A."
Find the probabilities for
1). no zero gold coins in Bag A
2). only 1 gold coins in Bag A
3). only 2 gold coins in Bag A
Thx again.
Find the probabilities for
1). no zero gold coins in Bag A
2). only 1 gold coins in Bag A
3). only 2 gold coins in Bag A
Thx again.
So... everything after "1. Find the probabilities of each possible numbers of gold coins, from 0 to 3, in bag A. " should be ignored?
ASKER
Let say in this way, what's the probability for 3 coins are sliver in bag A.
C(6,3) shows that there are in total 84 combination in bag A.
But, how to find to number of combination with only 2 coins are gold ? If I can solve this, I believe i can also know how to find any case where only 1 coins are gold or 3 are gold as well.
Thx
C(6,3) shows that there are in total 84 combination in bag A.
But, how to find to number of combination with only 2 coins are gold ? If I can solve this, I believe i can also know how to find any case where only 1 coins are gold or 3 are gold as well.
Thx
ASKER CERTIFIED SOLUTION
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You can also find the probabilities by constructing binary trees:
So the probability of picking three gold coins in a row is (3/9)*(2/8)*(1/7)
Can you see the factorials at work?
Or you can just multiply it out: 6/504 = 1/84 as shown earlier.
1st Coin 3/9 6/9
2nd Coin 2/8 6/8 3/8 5/8
3rd Coin 1/7 6/7 3/7 4/7 2/7 5/7 3/7 4/7
GGG GGS GSG GSS ...So the probability of picking three gold coins in a row is (3/9)*(2/8)*(1/7)
Can you see the factorials at work?
Or you can just multiply it out: 6/504 = 1/84 as shown earlier.
Without clarity in questions, accurate answers are very unlikely.