Question

You roll two dice (each die has six sides). What is the probability that you won't roll a 1 or a 6 on either die?A) 11.1%B) 66.7%C) 44.4%D) 69.4%

Answer 1

Answer: B) 66.7%

Step-by-step explanation:

We know that, Number of outcomes on a fair die = 6

When we throw two dice , the total number of possible outcomes = $6\times6=36$  (By Fundamental counting principle)

The outcomes having either a 1 or a 6 = (1 , 1) (1 ,2) , (1,3) , (1,4) , (1,5) , (1,6)

(6, 1) (6 ,2) , (6,3) , (6,4) , (6,5) , (6,6)

i.e. Total 12 outcomes have either a 1 or a 6 .

So , the number of outcomes do not have either a 1 or a 6 = 36-12=24

i.e. favorable outcomes = 24

Now , the  probability that you won't roll a 1 or a 6 on either die would become

$\dfrac{\text{P( Favorable outcomes )}}{\text{Total outcomes}}\\\\=\dfrac{24}{36}=\dfrac{2}{3}$

In percent = $\dfrac{2}{3}\times100=66.7\%$

Hence, the probability that you won't roll a 1 or a 6 on either die= 66.7%

Therefore ,  the correct answer is B) 66.7% .