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What is the probability of rolling a number greater than 4 on a number cube and then spinning an even number on a spinner divided into 12 equal sectors numbered 1 through 12?

 

(Answer with a simplified fraction please.)

 Dec 21, 2017
 #1
avatar+569 
+1

Let's start from the top:

There is a 1/36 chance of rolling a 2

There is a 2/36 chance of rolling a 3

There is a 3/36 chance of rolling a 4

Adding them up, we get 6/36, or 1/6.

Subtracting this from unity (1) we get 5/6.

There is a 1/12 chance of spinning a 2

There is a 1/12 chance of spinning a 4

There is a 1/12 chance of spinning a 6

There is a 1/12 chance of spinning a 8

There is a 1/12 chance of spinning a 10

There is a 1/12 chance of spinning a 12

Adding them up, we get 6/12, or 1/2

Multiplying the numerators and denominators horizontally, we get \(\tfrac{5}{12}\).

Did this help? I hope it did! smiley

 Dec 21, 2017
 #2
avatar+83 
0

That's wonderful, thank you.

RedBlue  Dec 21, 2017
 #3
avatar+111360 
+1

Assuming that  the number cube has the possible outcomes of1,2,3,4,5 or 6.....the probability of rolling a number >  4     =  [  2 favorable outcomes ] / [6 possible outcomes ]  =  2/6  = 1/3

 

And the probability of spinning an even number = 

[ 6 favorable outcomes] / [ 12 possible outcomes] =

6/12   =   1/2 

 

So....the probability  =  P(first event) * P(second event)  =  (1/3) * (1/2)   =  1/6

 

 

cool cool cool

 Dec 21, 2017

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