A reading list contains 3 historical books and 4 science-fiction books. What is the probability that Tena will...

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Kulla_9289

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A reading list contains 3 historical books and 4 science-fiction books. What is the probability that Tena will randomly choose a historical book for her first repost and a science-fiction book for her second?

a. 12/49

b.2/9

c.2/7

d.1 2/7

I got 3/7, but it's not an option. Any help will be appreciated.
 
Kulla_9289 said:
A reading list contains 3 historical books and 4 science-fiction books. What is the probability that Tena will randomly choose a historical book for her first report and a science-fiction book for her second?

a. 12/49

b.2/9

c.2/7

d.1 2/7

I got 3/7, but it's not an option. Any help will be appreciated.
Click to expand...
Can you tell us a little about your thinking?

Your answer is the probability of randomly selecting a historical book for the first report. That is not all you need.

After that, what books are left? What is the probability of selecting a science-fiction book for the second, given that?

Now, how do you combine those?
 
I used the probability tree method. After removing another science fiction and historical book, I get 1/7. However, 1/7 is not an option.
 
Kulla_9289 said:
A reading list contains 3 historical books and 4 science-fiction books. What is the probability that Tena will randomly choose a historical book for her first repost and a science-fiction book for her second?
Click to expand...
What in [imath]\dfrac{3}{7}\cdot\dfrac{4}{6}=~?[/imath] Why that?
 
Kulla_9289 said:
pka, that was my first guess until https://brainly.com/question/3451905#:~:text=is equal to-,2/7,-. The answer is destroyed it. I used probability tree to find it out afterwards. I think there is an easier method than that "permutation" thing.
Click to expand...
But what pka said gives the same answer, 2/7. What do you mean by "destroyed"?

There are many ways to solve it. Permutations, as used in the answer you refer to, are one; multiplying probabilities is another; probability trees are another. All give the same result, when used correctly.

What we'd like to do is to help you avoid whatever specific mistakes you made that led to the wrong answers 3/7, and then 1/7. Would you care to show us your details, so we can help you more?
 
This attachment is for 3/7. "pka, that was my first thought till I saw this. After that, I utilised a probability tree to figure it out. I believe there is a simpler approach than "permutation."
 

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Kulla_9289 said:
This attachment is for 3/7. "pka, that was my first thought till I saw this. After that, I utilised a probability tree to figure it out. I believe there is a simpler approach than "permutation."
Click to expand...
Thanks for showing this. Presumably you see that what you calculated there is the probability of choosing the same genre both times, rather than choosing history followed by SF:

1650371574955.png

Following the yellow line, you get to the correct answer.
 
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