Question

Students in a school were surveyed about their study habits. Forty-two percent of students said they study on weeknights and weekends, 47% said they studied on weekends, and 65% said they study either on weeknights or weekends. If you were to pick one student at random, what is the probability that he or she studies on a weeknight?

Answer 1

I usally know that umm hold up

Answer 2

kk

Answer 3

This is how I'm visualizing the data.

The first bar expresses 100% of the students.
The second bar expresses the 42% who study on weeknights and weekends
The third bar expresses the 47% who study on weekends
The fourth bar expresses the 65% who study on weeknights or weekends.

Answer 4

What's confusing to me is how they don't add up to 100%, and there are situations of overlap with the %, where 65 + 47 = 112, so there will be 12% of those who study on weeknights or weekends who also said that they studied on weekends?

Answer 5

Yeah. That's what I'm confused about 2. The unit name is, Theoretical, Experimental, and Compound Probabilities, if that helps any. lol

Answer 6

Yeah I honestly haven't learned how to represent this kind of statistics. I'll tag the people smarter than me as I'm genuinely curious how this would be solved. I'm sure it's simple I just can't see it. @Hero @Vocaloid @Zarkon

Answer 7

meant to say probabilities lol

Answer 8

lol yeah Thanks!

Answer 9

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Shadow
Yeah I honestly haven't learned how to represent this kind of statistics. I'll tag the people smarter than me as I'm genuinely curious how this would be solved. I'm sure it's simple I just can't see it. @Hero @Vocaloid @Zarkon
\(\color{#0cbb34}{\text{End of Quote}}\)
*gasp* There are smarter people than you? noooooooooooooo XD literally impossible! XD

Answer 10

right?

Answer 11

XD lolllll

Answer 12

This is sum rule probability:
\(P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)\)

In this case, \(P(A)\) represents percentage of students studying on weekends. \(P(B)\) represents percentage of students studying on weeknights.

Answer 13

How do we figure out how many for weeknights? Plug in everything other than P(B)?

Answer 14

Correct and then isolate \(P(B)\). Technically, you're supposed to isolate \(P(B)\) first.

Answer 15

Okay! Great! Thank you so much! This really helps a lot! I really appreciate it!

Answer 16

Hold on a minute. Before you go, let's make sure you have the correct answer. Can you tell us what is \(P(B)\) ?

Answer 17

Imma solve it rq. just a sec...

Answer 18

P(B)=60% ?????

Answer 19

Correct.

Answer 20

Great! Thank you so much! I also had another problem. Aqual posted it for me above, if you could take a look at it, that would be great! :)

Answer 21

Kinda tight on time unfortunately. Next time though

Answer 22

Okay! Thank you!