Question

Two symmetric dice have had two of their sides painted red, three painted black, and the other one painted white. When this pair of dice is rolled, what is the probability that both dice land with the same color face up?

Answer 1

It is given that dice had two of their sides painted red, three painted black, and the other one painted white

Thus, P(red for one) = 2/6 = 1/3

P((black for one) = 3/6 = 1/2

P(while for one) = 1/6

Thus,

P(red for both) = 1/3*1/3 = 1/9

P((black for one) = 1/2*1/2 = 1/4

P(while for one) = 1/6*1/6 = 1/36

Now, P(both dice land with the same color face up)

= P(red for both) + P(black for both) + P(white for both)  

= 1/9 + 1/4 + 1/36

= (4+9+1)/36

= 14/36

= 7/18

= 0.39