Question

Derek flips a coin and rolls a number cube at the same time. Derek rolls an even number. Find the probability that the coin came up heads and the number cube roll was a 2.

A: 3/4

B: 2/3

C: 1/12

D: 1/4

Answer 1

Well given the answers given.. it seems like they don't care about the fact that an even number was rolled (this information is given..) Because using that information, then you know:
You are given that the roll was even, so the sample space for the cube is {2, 4, 6}.

Now the probability of getting a heads is 1/2
The probability of getting a 2 from {2, 4, 6} is 1/3

So, the probability of heads AND a "2" = (1/2)*(1/3) = 1/6

However... If they ignore the fact that they rolled and even number, then the probability of getting a "2" is just 1/6, so the overall probability of heads AND a "2" = (1/2)*(1/6) = 1/12

Answer 2

That's what I got also, however, I forgot to mention that the answer was 1/4. I just wanted to know the explanation for this question.

Answer 3

I also got the question wrong.

Answer 4

1/4 o.o? did they even give an explanation

Answer 5

Nope.

Answer 6

But, this was under the subject: Conditional Probability. So the answer may be from the formula of conditional probability.

Answer 7

Well what I did is the same as conditional probability.. if you want to use the definition.. it will give the same result (conditional probability means that you are restricting your sample space to a smaller subset of given values)
Let H = heads
T = getting "two"
and "E" = even number
You are interested in:
\[ P(H \cap (T|E))\]
\[ P(T|E)=\frac{{P(T \cap E})}{P(E)}\]
\(T\cap E =\{2\}\\
E = \{2, 4, 6\}\)
So,
\[ P(T|E)=\frac{P(\{2\})}{P(\{ 2, 4, 6\})}=\frac{1/6}{3/6}=1/3\]

Answer 8

so \(P(H \cap (T|E))\)=\(P(H)P(T|E)=(1/2)(1/3)=1/6\) we just multiply since the events are independent

Answer 9

I got all of those answers that you found, but for some reason the answer for the question is 1/4.

Answer 10

I feel like this is an error.. or they missed something in the question :S Hopefully you can ask your teacher for an explanation.

Answer 11

Alright, thank you anyway.

Answer 12

yw, good luck!