Question 1210208: A jewelry box contains two gold hoop earrings and two silver hoop earrings. You randomly choose two earrings. What is the probability that both are silver hoop earrings? Write your answer as a simplified fraction.
Found 5 solutions by Edwin McCravy, ikleyn, mccravyedwin, greenestamps, EPM:
Answer by Edwin McCravy(20056)   (Show Source):
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The sample space is composed of the 6 choices:
{S1S2, S1G1, S1G2, S2G1, S2G2, G1G2}
The successful space is {S1S1}
Probability: 1/6
Edwin
Answer by ikleyn(52794)  (Show Source):
Answer by mccravyedwin(407)  (Show Source):
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Ikleyn is wrong. She is thinking that just because we humans cannot tell the
difference between two earrings that look identical to us, that they are exactly
the same two things. But they are not. Put them under a microscope and you
will find they are quite different things.
Think of putting a tiny label on each earring, the labels being S1,S2,G1,G2.
Would that make it less likely to choose the pair labeled (S1,S2)? No, it would
not!! But in Ikleyn's way of thinking here it would be.
If she will think about it long and hard she will understand that the
probability of getting two silver hoop earrings is exactly the same, 1/6,
whether labels were placed on the earrings or not.
It should be brought to Ikleyn's and everybody's attention that NO TWO THINGS
ARE REALLY AND TRULY INDISTINGUISHABLE! Not under a microscope!
Even though many math problems state that things are indistinguishable, that
only means that they are talking about the way they look to us humans. But in
reality, no two things are exactly alike. Not exactly!!
The word "indistinguishable" should only and always be taken to mean
"indistinguishable TO HUMANS' EYES".
In math problems that deal with "indistinguishable things", they are always
speaking of the number of different ways we humans would consider two things to
appear different to our human eyes. They are not speaking of two things being
exactly alike atom by atom, for no two things are exactly alike.
A jewelry box contains two gold hoop earrings and two silver hoop
earrings.
There are four different things, whether some of them look the same to us humans
or not.
1. S1, silver hoop earring #1
2. S2, silver hoop earring #2
3. G1, gold hoop earring #1
4. G2, gold hoop earring #2
You randomly choose two earrings.
The possible choices are
1. S1 and S2 <-- the only choice that they are both silver hoop earrings
2. S1 and G1
3. S1 and G2
4. S2 and G1
5. S2 and G2
6. G1 and G2
What is the probability that both are silver hoop earrings?
The only choice that contains both silver hoop earrings is choice 1 above.
That's 1 choice out of 6.
Write your answer as a simplified fraction.
The probability is 1/6.
Edwin
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Tutor ikleyn has recently been posting wrong answers to relatively simple problems and posting disparaging comments about solutions that are correct, then having to eat crow and apologize when she realizes her solution is wrong. Sad....
This is a quite basic probability problem. We need to choose 2 of the 4 earrings, and the desired outcome is that we choose 2 of the 2 silver hoop earrings and 0 of the 2 gold hoop earrings. Using the basic definition of probability, the probability is
We can also get that result analyzing the problem as choosing one earring at a time.
The probability that the first earring is silver hoop is 2/4; then the probability that the second earring is the other silver hoop is 1/3. The probability that they are both silver hoop is then
Answer by EPM(3)  (Show Source):
You can put this solution on YOUR website!
Thanks, greenestamps! I think Ikleyn knows by now she had a brain fart on this
problem. I've had my share of 'em! And I'll bet greenestamps has had a couple
too.
But Ikleyn is being a narcissist. Not only that but she's also being a bully.
Those two traits are known to go together. Think of our president!
Ikleyn knows mathematics, and greenestamps and I both know she does. We're not
saying she doesn't! So, there is no way Ikleyn could STILL believe that labeling
the earring hoops could decrease the probability of getting both silver ones!
Ikleyn, please try to realize that having brain farts is nothing to be ashamed
of. Here is the problem you solved instead of the one given.
A jewelry box contains two gold hoop earrings and two silver hoop earrings. You
notice that there are only 3 kinds of pairs to choose:
1. Two Silvers, SS.
2. Two Golds, GG.
3. One silver and one gold, SG.
You take three slips of paper and write SS on one, GG on one, and SG on one.
You then put those slips of paper in a box, shake the box, and then draw one.
What is the probability that you will get the slip of paper with SS written on
it?
Of course, the answer is 1/3.
That is the problem that you essentially solved, But that is not the problem
that is stated.
Ikleyn, please try to realize that everybody has brain farts. I've had some
just as foolish as this one -- over just as simple a problem as this.
One thing they teach you in the Dale Carnegie course is this: If you're wrong,
admit it, quickly and emphatically.
That big ego of yours is not going to bring you happiness or get you more
praise. In simpler words, be nice to everybody! Don't put the students down
if they mistype or forget something. They're humans too, and they have brain
farts. If you need to bully, just keep bullying that AI tutor. He's not a
human. His errors can't be blamed on brain farts, but just what he hasn't yet
learned.
Edwin
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