An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.Compute the probability of each of the following events.Event A: The sum is greater than 5.Event B: The sum is an odd number.Write your answers as fractions.
Question
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.Compute the probability of each of the following events.Event A: The sum is greater than 5.Event B: The sum is an odd number.Write your answers as fractions.
Solution
To solve this problem, we first need to understand the total number of possible outcomes when rolling a die twice. Since a die has 6 faces, the total number of outcomes is 6*6 = 36.
Event A: The sum is greater than 5. The possible outcomes where the sum is greater than 5 are: (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6). That's 24 outcomes. So, the probability of the sum being greater than 5 is 24/36 = 2/3.
Event B: The sum is an odd number. The possible outcomes where the sum is an odd number are: (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5). That's 18 outcomes. So, the probability of the sum being an odd number is 18/36 = 1/2.
Similar Questions
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.Compute the probability of each of the following events.Event A: The sum is greater than 8.Event B: The sum is divisible by 4 or 6 (or both).Write your answers as fractions.(a) PA = (b) PB =
Below is a list of all possible outcomes in the experiment of rolling two die.Note: The table gives the values of each die, not the sum of the two die.Determine the following probabilities. Write your answers as reduced fractions.P𝑃 (sum is odd) = P𝑃 (sum is 5) = P𝑃 (sum is 7) =
Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number. Enter your probabilities as fractions.)(a)rolling an even sum
What is the probability of rolling an odd number of dots with a fair, six-sided die numbered one through six? (Enter your probability as a fraction.)
You are rolling a fair six-sided die. What is the probability of rolling an odd number or a number less than 4?A.1/3B.2/3C.1/2D.5/6
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.