Question

Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain

Answer 1

A wheel with six sections labeled 1 through 6 means there's a 1/6 chance of landing a 5.

A cube as six faces, so there's a 1/6 chance of getting one given number. Since two cubes must roll the same number sequentially in order for her to win, this is her chance:

\[\frac{ 1 }{ 6 } \times \frac{ 1 }{ 6 } = \frac{ 1 }{ ? }\] If you can solve for the denominator, you can see that this is a much smaller chance than 1/6

Answer 2

Here is a way you can visualize it
\[P(A) \times P(B) = P(A B)\]

The probability of A happening times the probability of B happening is the probability of both A and B happening.

Answer 3

Why do many people say the probability of the cubes is 6/36?

Answer 4

idk, that's weird

Answer 5

6/36 simplifies to 1/6, but idk why they would do that

Answer 6

Oh actually, I see my error. I was assuming that she would have to get 5 twice. But that's not true.

Answer 7

No - Problem! Can you please provide on how I could find 6/36 as the probability?

Answer 8

She just has to get the same number twice. So 1 on both cubes. 3 on both cubes, etc.

So since the total outcomes of rolling the cubes is 36, and there are 6 pairs of numbers, that's how they get 6/36.

Answer 9

Each of the pairs: 1:1, 2:2, 3:3, 4:4, 5:5, 6:6

But there's a 1/36 chance of each of those events happening. Add up all those possible events and you get 6/36 which simplifies to 1/6. So there's an equal chance between both the wheel and the cubes.

Answer 10

Sorry I'm hungry and currently waiting on food. Brain derped earlier (:

Answer 11

Let me know if this makes sense

Answer 12

Yes - thank you very much (: