Question

Henry rolls 2 number cubes numbered 1 through 6 while playing his favorite board game. He will get a second turn if he rolls a sum that is an even number less than 10. What are Henry's chances of getting a second turn when he rolls the number cubes? 7/18 11/18 5/36 17/36 I got 5/18. I added up the amount of different ways to get 2-8. I found 10. Either the test is wrong or I'm really bad at counting, and I'm not confident enough to count either of them out.

Answer 1

First of all, we know that each cube can land in 6 different ways,
so two cubes can land in (6x 6) = 36 different ways.

Now let's check your count.  How many ways can you roll a 2, 4, 6, or 8 ?

Cube-A  Cube-B
      1            1              2
      1            3              4
      3            1              4
      2            2              4
      1            5              6
      5            1              6
      2            4              6
      4            2              6
      3            3              6
      2            6              8
      6            2              8
      3            5              8
      5            3              8
      4            4              8

I get 14 ways.

So the probability of success is

         (number of successful ways) / (total possible ways) =

                       (14)                            /            (36)                  =  7/18 .

Answer 2

Answer: $\frac{7}{18}$

Step-by-step explanation:

The sample size n ( total pairs )=$6\times6=$36

Pairs having the even sum less than 10 area

(1,3), (3,1), (1,5), (5,1),(3,5),(5,3),

(2,4), (4,2), (2,6),(6,2),

(1,1),(3,3),(2,2),(4,4)

The number of ways to get a sum that is an even number less than 10= 14

The chances of getting a second turn when he rolls the number cubes=$=\frac{\text{favourable outcomes}}{\text{Total outcomes}}\frac{14}{36}=\frac{7}{18}$

Hence, The chances of getting a second turn when he rolls the number cubes=$\frac{7}{18}$