Maggie has 7 tiles with pictures of plants and 2 tiles with pictures of animals. Maggie keeps all the tiles on a mat with the pictures hidden and mixes them up. She then turns one tile face up and finds the picture of a plant on it. She removes this tile from the mat and turns over another tile without looking. What is the probability that the second tile that Maggie turns over has a plant on it?

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Maggie has 7 tiles with pictures of plants and 2 tiles with pictures of animals. Maggie keeps all the tiles on a mat with the pictures hidden and mixes them up. She then turns one tile face up and finds the picture of a plant on it. She removes this tile from the mat and turns over another tile without looking. What is the probability that the second tile that Maggie turns over has a plant on it?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Let me try it. First, let's draw a probability tree:|dw:1443247540178:dw| where P represents the probability of plants and A the probability of animals. There are total of 9 tiles so for the first pick the probability of picking a plant is 7/9 and 2/9 for picking an animal. Suppose the first pick is a plant and this tile has been removed from the mixture (as stated in the problem) , the probability of picking a plant and an animal for the second time is now equal to 6/8 and 2/8, respectively.
We're interested in the encircled part of the probability tree since it is stated that the first pick is a plant. |dw:1443248009893:dw|, then for the second time:\[P(plant)=\frac{ (\frac{ 7 }{ 9 })(\frac{ 6 }{ 8 }) }{ (\frac{ 7 }{ 9 })(\frac{ 6 }{ 8 })+\frac{7 }{ 9} (\frac{2}{8})}=3/4\] I'm not 100 % sure about this though. others can correct if I'm wrong but I think this is correct. :)

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