Answer:
21/72 = 0.2917 = 29.17% probability that a 6 is rolled both times
Step-by-step explanation:
Two have faces numbered 1,2,3,4,5, and 6
So for these two, each with 1/4 probability of being chosen, the probability of rolling two six is given by:
(1/6)^2 = 1/36
So
[tex]p_A = 2 \times \frac{1}{4} \times \frac{1}{36} = \frac{1}{72}[/tex]
One has faces numbered 2,2,4,4, 6 and 6;
The probability of rolling 2 faces six with this dice is:
(2/6)^2 = 4/36
This dice has 1/4 probability of being chosen. So
[tex]p_B = \frac{1}{4} \times \frac{4}{36} = \frac{1}{36}[/tex]
One has all six faces numbered 6.
The probabilityu of rolling two six is given by:
(6/6)^2 = 1^2 = 1
This dice has 1/4 probability of being chosen. So
[tex]p_C = \frac{1}{4} \times 1 = \frac{1}{4}[/tex]
Calculate the probability that a 6 is rolled both times
[tex]p = p_A + p_B + p_C = \frac{1}{72} + \frac{1}{36} + \frac{1}{4} = \frac{1 + 2 + 18}{72} = \frac{21}{72}[/tex]
21/72 = 0.2917 = 29.17% probability that a 6 is rolled both times
