Question

At a high school, the probability that a student takes a science class and a history class is 0.48. The probability that a student takes a science class is 0.82, and the probability that the student takes a history class is 0.64. What is the probability (rounded to the nearest hundredth) that a student takes a history class given that the student is taking a science class?

0.39
0.75
0.30
0.59

Answer 1

start with the formula that a prob of something (say, A) given something else (say, B) is \[P(A|B)=\frac{P(A,B)}{P(B)}\]

Answer 2

can you identify what is A and B in the wording?

Answer 3

Not really. which is which?

Answer 4

P(A|B) --> P(takes history | taking science) , so A corresponds to taking history, B corresponds to taking science

Answer 5

P(A,B) is the probability that a student is taking *both*

Answer 6

P(B) is the prob that a student is taking science (irregardless of whether she takes history or not)

Answer 7

now you can plug the numbers into the formula

Answer 8

I am getting 0.58537 which, rounded up, looks like (d)

Answer 9

How did you get there? If you don't mind me asking

Answer 10

0.48/0.82

Answer 11

0.48 is the P(A,B) and 0.82 is P(B)

Answer 12

does it make sense?

Answer 13

Yes that makes sense

Answer 14

OK thank you! I have one more. Would you mind helping me with it?

Answer 15

yes

Answer 16

i mean go ahead

Answer 17

The probability that you roll a 3 on a six sided die is 1/6. The probability that you flip a coin that lands on tails is 1/2. The probability that you roll a 3 on a six-sided die and you flip a coin that lands on tails is 1/12. What is the probability of flipping a coin and it landing on tails, given that you rolled a 3 on a six-sided die? Are these two events independent?

Answer 18

The answer choices:

P(T, 3) = 1/12; therefore, events are independent because P(T, 3) = P(T)
P(T, 3) = 1/6; therefore, events are dependent because P(T, 3) doesn't equal P(T)
P(T, 3) = 1/3; therefore, events are dependent because P(T, 3) doesn't equal P(T)
P(T, 3) = 1/2; therefore, events are independent because P(T, 3) = P(T)

Answer 19

do you have any guess on your mind?

Answer 20

This one seems to be really hard for me. I feel like it would be independent, but I am not sure whether it's 1/12 or 1/2.

Answer 21

your intuition is correct, they are independent. Given that the roll is 3, it is still same odd of 1/2 to see the coin landing tail.

Answer 22

the important word here is "given"

Answer 23

if it was "and" (as in "roll a 3 and land tail") that would be that 1/12

Answer 24

makes sense?

Answer 25

Yes thank you!

Answer 26

yw