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 Subject: math/adding probabilities Name: spencer Who are you: Teacher i have a math ? that me and my dad do not get we know the answer is 5/6 but we do not get how to get their so here is the problem lisa has 9 rings in her jewelry box. five are gold and 4 are silver. if she randomly select 3 rings to wear to a party, find each probability p(2 silver or 2 gold) and or i know means to add and and means to mult.   thank you for any help you can give us

Hi Spencer.

Your question is worded strangely, so we can reword it as follows:

Since there are two types of rings and Lisa is taking three rings, you will certainly have a pair, but the third ring may match the pair or may not match the pair. So really we are asking, what is the
probability that Lisa does not get three of a kind?

It should be clear to you that this is just one minus the chances she does get three of a kind. Since it is easier to calculate the chances she gets three of a kind, let's use this approach.

The chances she gets three gold rings:

The first ring is chosen from 9, of which 5 are gold, so we have 5/9.
The second ring is chosen from 8 remaining rings, of which 4 are gold, so we have 4/8.
The third ring is chosen from 7 remaining rings, of which 3 are gold,so we have 3/7.
Multiply these together to get the chances that she pulls out three gold rings in a row:
5/9 x 4/8 x 3/7.

The chances she gets three silver rings:

The first ring is chosen from 9, of which 4 are silver, so we have 4/9.
The second ring is chosen from 8 remaining rings, of which 3 are silver, so we have 3/8.
The third ring is chosen from 7 remaining rings, of which 2 are silver, so we have 2/7.
Multiply these together to get the chances that she pulls out three silver rings in a row:
4/9 x 3/8 x 2/7.

What are the chances she pulls out either a gold triple or a silver triple? We add them:
( 5/9 x 4/8 x 3/7 ) + ( 4/9 x 3/8 x 2/7)

And so the probability she pulls out a pair and an odd ring is one minus this:
1 - ( ( 5/9 x 4/8 x 3/7 ) + ( 4/9 x 3/8 x 2/7) )

which, as you indicated, works out to 5/6.

Hope this helps,
Stephen La Rocque.

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