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 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

what is the probability of winning at the wheel?

Answer 2

Either method is equally likely. They both will produce a success at:

Probability = 1/6

The spin will give success at 1 out of 6

The dice roll will give success at 6 out of 36 -> 1 out of 6

They are equal as far as probability goes.

Answer 3

the probability of rolling a 6 on a die is 1/6
the probability of rolling a 6 on a 2nd die is 1/6

isnt probability of rolling both 1/6 * 1/6

Answer 4

@Jim766 Yes it is

Answer 5

1/6*1/6 = 1/36

Answer 6

A little bit more about the dice rolls:

There are 36 different dice rolls: any of 6 #'s on 1 die multiplied by any of 6 #'s on the other die. 6 x 6 = 36. And there are only 6 different rolls where both #'s are the same:

1,1 2,2 3,3 4,4 5,5 6,6

Answer 7

so which is better probability 1/6 or 1/36?

Answer 8

Spinnig wheel P(of getting a 5) 1/6
Number cube = 6 sides
2 number cubes = 6*6=36 and probaibily is 6 of getting same number
6/36 u can divide by 6 to get 1/6 same chance

Answer 9

That's why the P(2 same #'s) = 1/6 -> 6 out of 36 = 1/6

And as for getting a "5" when spinning: 1/6

That's why the two activities give the same probability.

Answer 10

@Jim766 ,the dice roll situation is not calling for both #'s to be a "5". It is calling for both numbers to be the same, so it's not 1/36, it's 6/36 = 1/6

Answer 11

ahh so the difference is that they were not specific about what number had to be rolled...

Answer 12

Actually they were specific in not requiring any particular number. That lack of that particular requirement is in itself a "specificity".

Answer 13

Therefore, she could pick either one and get the same chance of winning no matter which one she picks?

Answer 14

That's right!

Answer 15

Thanks!

Answer 16

uw! Good job everyone!

Answer 17

All good now, @mangorox ?

Answer 18

Yes, thanks @tcarroll010 !

Answer 19

Good luck in all of your studies! @mangorox