For a carnival game, a cube is rolled.Each of its six faces has a different color. To win,you must select the color rolled.Find the probability of playing the carnival game twice and winning both times.

B.suppose for the game,you choose red and your friend picks blue. What is the probability that either you or your friend wins?

The probability of any color = 1/6.

A. If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

B. Either-or probabilities are found by adding the individual probabilities.

To find the probability of winning the carnival game twice, we need to multiply the probabilities of winning each game individually.

The probability of winning the carnival game once is 1 out of 6, since there are 6 different colors and only one will be rolled.

Therefore, the probability of winning the carnival game twice is (1/6) * (1/6) = 1/36.

Now, let's calculate the probability that either you or your friend wins the game.

First, let's calculate the probability that you win and your friend loses. The probability of you winning is 1/6, and the probability of your friend losing is 5/6 (since there are 5 colors other than blue). Therefore, the probability of this event is (1/6) * (5/6) = 5/36.

Next, let's calculate the probability that your friend wins and you lose. The probability of your friend winning is 1/6, and the probability of you losing is 5/6 (since there are 5 colors other than red). Therefore, the probability of this event is (1/6) * (5/6) = 5/36.

Since the events of you winning and your friend winning are mutually exclusive (they cannot both happen at the same time), we can add the probabilities of these two events:
P(either you or your friend wins) = P(you win and your friend loses) + P(your friend wins and you lose)
P(either you or your friend wins) = 5/36 + 5/36
P(either you or your friend wins) = 10/36

Therefore, the probability that either you or your friend wins the game is 10/36, which can be simplified to 5/18.

To find the probability of winning a carnival game twice in a row, where each face of the cube has a different color, we need to consider the probability of winning each individual game separately and then multiply those probabilities together.

1) Probability of winning a single game:
Since there are six different colors on the cube, the probability of rolling the correct color in one attempt is 1/6.

2) Probability of winning both games:
Since the games are independent events, the probability of winning both games is calculated by multiplying the probability of winning each game together.
So, the probability of winning both games is (1/6) * (1/6) = 1/36.

Now, let's move on to the second part of the question.

To find the probability that either you or your friend wins when you choose red and your friend picks blue, we need to calculate the probability of you winning plus the probability of your friend winning and then subtract the probability of both winning.

1) Probability of you winning:
As discussed earlier, the probability of winning a single game by selecting the correct color is 1/6. So, your probability of winning is 1/6.

2) Probability of your friend winning:
Similarly, the probability of your friend winning a single game by selecting the correct color (blue) is also 1/6.

3) Probability of both winning:
Since you and your friend have different colors, the probability of both winning at the same time is 0. Therefore, the probability of both winning is 0/36 = 0.

Now, let's calculate the probability that either you or your friend wins:
Probability = Probability of you winning + Probability of your friend winning - Probability of both winning
Probability = (1/6) + (1/6) - 0 = 2/6 = 1/3.

Therefore, the probability that either you or your friend wins is 1/3.