Question

The probability that a student passes mathematics class is 0.75, the probability that he passes history class is 0.80, and the probability that he passes mathematics and history is 0.60. Are the two events independent of each other?

Answer 1

A. Yes, they are independent because P(M) ⋅ P(H) = P(M ∩ H)
B. No, they are dependent because P(M) ⋅ P(H) = P(M ∩ H)
C.Yes, they are independent because P(M) ⋅ P(H) ≠ P(M ∩ H)
D. No, they are dependent because P(M) ⋅ P(H) ≠ P(M ∩ H)

Answer 2

You can multiply the probability of events if they are linked.
Multiply the probabilities and see if it equals 0.6 to determine if they are dependent or independent.

eg: flipping a coin gives a 1/2 chance of yielding heads. Flipping 2 coins gives a 1/4 (1/2x1/2) change of yielding two heads

Answer 3

if \[P(M)\times P(H)=P(M\cap H)\] then they are independent
if not , then they are dependent

Answer 4

Do you understand the notation used? (i.e. the "upside down u" and everything)

Answer 5

I think so do i do .75 x .60=.45

Answer 6

no, use the probability of the individual subjects

I.e. P(math) x P(history) = 0.75*0.8 = ?

Answer 7

p(m)xP(H)=0.6

Answer 8

so p(m) x p(h) is equal to p(m+h). Does that make them dependent or independent?

Answer 9

it makes them dependent?

Answer 10

is \[.80\times .75=.60\]? it either is, or it is not

Answer 11

it is .60

Answer 12

so there are equal right?

Answer 13

that makes the events "independent"

Answer 14

oh ok

Answer 15

so the answer would be Yes, they are independent because P(M) ⋅ P(H) = P(M ∩ H)

Answer 16

that's correct!

Answer 17

ok thanks could u help me with one more?

Answer 18

sure!

Answer 19

thx give me a sec

Answer 20

There is a 70% chance that your car will get stuck in the snow during the next big snowfall. Given that you are already stuck in the snow with your car, the chance that you will require a tow truck to pull you out is 90%. What is the chance that you will get stuck in the snow with your car and will require a tow truck to pull you out?

Answer 21

how would i solve this?

Answer 22

multiply the probabilities - IF you go out, there is a 0.7 chance you get stuck in the snow. IF you get stuck, there is a 0.9 chance you need a tow truck. The probability of both is like the coin example above, so just multiply them together.

Answer 23

ok so it would be 0.63% ?

Answer 24

yep!

Answer 25

could you check to see if i go this right i picked c

One vase of flowers contains eight purple tulips and six yellow tulips. A second vase of flowers contains five purple tulips and nine yellow tulips. An example of dependent events is selecting a purple tulip from the first vase and then selecting a ____________ .
.

A. yellow tulip from the same vase, without replacing the first tulip
B.purple tulip from the same vase, after replacing the first tulip
C.yellow tulip from the second vase
D. purple tulip from the second vase

Answer 26

@wilsondanielle

Answer 27

which of these do you think depend on one another?
a) same system, NOT reset
b) same system, reset
c) different system
d) different system

you're looking for something that is affected by the first action

Answer 28

A?

Answer 29

A is the only one affected by the first tulip (because it is now missing, DECREASING the chance of drawing a purple tulip and INCREASING the chance of drawing a yellow tulip) so it would be correct

Answer 30

so the answer would be a and not c?

Answer 31

yes. C is independent because it's in a different system - anything that happens in vase A doesn't affect Vase B because they aren't attached.

Answer 32

ok thanks so much ur awesome

Answer 33

no problem!