dependent probability

[teachme]

Sarah has 24 pictures. 10 are of her. The rest are of Kim. Sarah will draw 5 pictures out. The first 4 are of Sarah. What is the probability that the last one is of Kim?

The answer that I keep coming up with is not a choice to the question. I also have to show the work of how i got my answer. Your help would be greatly appreciated. Thanks

 

[Deleted member 4993]

Sarah has 24 pictures. 10 are of her. The rest are of Kim. Sarah will draw 5 pictures out. The first 4 are of Sarah. What is the probability that the last one is of Kim?

The answer that I keep coming up with is not a choice to the question. I also have to show the work of how i got my answer. Your help would be greatly appreciated. Thanks

What answer did you get and how did you get it?

Please share your work - so that we may know where to begin to help you.

 

[teachme]

I had Sarah at 10/24. Kim at 14/24. Then when Sarah picked out 4 of her own I changed the fractions to: 6/20 for Sarah and 14/20 for Kim. Then I multiplied them together: 6/20 x 14/20 and got 84/400 which I reduced to: 42/200 then 21/100.

 

[soroban]

Hello, teachme!

The problem is simple enough.
Exactly where is your difficulty?

Sarah has 24 pictures: 10 are of her, the rest are of Kim.
Sarah will draw 5 pictures out. .The first 4 are of Sarah.
What is the probability that the last one is of Kim?

There are 24 pictures: 10 of Sarah, 14 of Kim.

Four pictures of Sarah are drawn.
Now there are 20 pictures: 6 of Sarah, 14 of Kim.

What is the probability that the next draw will be a picture of Kim?

\(\displaystyle \text{It certainly looks like: }\:\frac{14}{20} \,=\,\frac{7}{10}\)


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Actually, the problem is rather silly.
That stuff about "Sarah drawing 5 pictures" is smoke-and-mirrors,
. . designed to confuse us.

The problem could have been:

. . There are 20 pictures: 6 of Sarah, 14 of Kim.
. . . . It doesn't matter who has them.

. . Someone draws one picture at random.
. . . . It doesn't matter who draws it.

. . What is the probability that it is a picture of Kim?