A six-sided die has 2 blue faces, 1 red face and 3 yellow faces. If the die is rolled twice, what is the probability that both rolls will result in a blue face?
P(blue) = 2/6 = 1/3
since the two rolls are independent,
P(blue,blue) = 1/3 * 1/3
To find the probability of both rolls resulting in a blue face, we need to determine the probability of rolling a blue face on each individual roll and then multiply those probabilities together.
The total number of faces on the die is 6. Out of those 6, there are 2 blue faces, so the probability of rolling a blue face on one roll is 2/6, which simplifies to 1/3.
Since we are rolling the die twice, we multiply the probabilities together. Therefore, the probability of rolling a blue face on both rolls is (1/3) * (1/3), which simplifies to 1/9.
So, the probability that both rolls will result in a blue face is 1/9.