Please help me with this homework
you roll two fair dice, a green one and a red one?
(a) are the outcomes on the dice independent?
(b)Find P(1 on green die and 2 on red die)
(c)Find P(2 on green die and 1 on red die)
(d)Find P(1 on green die and 2 on red die) or (2 on green die and 1 on red die)
(a) yes
(b) If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1/6 * 1/6 = ?
(c) same odds
(d) Either-or probabilities are found by adding the individual probabilities.
Sure, let's break down each part step by step:
(a) To check if the outcomes on the dice are independent, we need to determine if the outcome of rolling one die affects the outcome of rolling the other die. In this case, since the two dice are fair, the outcome of one die does not affect the other die. So, the outcomes on the dice are indeed independent.
(b) To find the probability of rolling a 1 on the green die and a 2 on the red die, we need to multiply the probabilities of each event. The green die has 6 possible outcomes (1, 2, 3, 4, 5, and 6), and the red die also has 6 possible outcomes. Since both dice are fair, each outcome is equally likely. Therefore, the probability of rolling a 1 on the green die is 1/6, and the probability of rolling a 2 on the red die is also 1/6. To find the probability of both events happening, we multiply these probabilities together: (1/6) * (1/6) = 1/36.
(c) Following the same logic, to find the probability of rolling a 2 on the green die and a 1 on the red die, we again multiply the probabilities of each event. The probability of rolling a 2 on the green die is 1/6, and the probability of rolling a 1 on the red die is also 1/6. So, the probability of both events happening is (1/6) * (1/6) = 1/36.
(d) To find the probability of rolling a 1 on the green die and a 2 on the red die or rolling a 2 on the green die and a 1 on the red die, we can add the probabilities of these two separate events since they are mutually exclusive. From parts (b) and (c), we already know that the probability of each event is 1/36. Therefore, the probability of either event happening is 1/36 + 1/36 = 2/36 = 1/18.
Remember, when adding or multiplying probabilities, make sure to use the correct rules based on the situation (e.g., mutually exclusive events or independent events).