Give the probability distribution for the indicated random variable. HINT [See Example 3.] (Enter your probabilities as fractions.) A red die and a green die are rolled, and X is the sum of the numbers facing up. x 2 3 4 5 6 7 8 9 10 11 12 P(X = x) Calculate P(X ≠ 11). (Enter your probability as a fraction.) P(X ≠ 11) =
Suppose that a red die and a green die are tossed and the numbers on the sides that face upward are observed (a) What is the probability that the numbers add up to 9? (b) What is the probability that the sum of the numbers is less than 5? (a) The probability that the sum of the numbers is 9 is (Type an integer or a simplified fraction)
If we roll a red 6-sided die and a green 6-sided die (both are fair dice with the numbers 1-6 equally likely to be rolled), what is the probability that we get (i) A 5 on the green die AND a 3 on the red die? (ii) A 5 on the green die OR a 3 on the red die? (iii) A 5 on the green die GIVEN we rolled a 3 on the red die?
4. Three fair dice have different colors: red, blue, and yellow. These three dice are rolled and the face value of each is recorded as R, B, Y, respectively. (a) Compute the probability that B< Y < R, given all the numbers are different; (b) Compute the probability that B< Y< R.
You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(5 on green die and 3 on red die). (Enter your answer as a fraction.) 2 (c) Find P(3 on green die and 5 on red die). (Enter your answer as a fraction.) 3 (d) Find P((5 on green die and 3 on red die) or (3 on green die and 5 on red die)). (Enter your answer...
A 20-sided fair die and an 8-sided fair die are rolled. What is the probability of rolling: exactly a 5 on the first die OR a 2 or larger on the second die? Enter your answer as a reduced fraction. ________________
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
Suppose that a red die and a green die are tossed and the numbers on the sides that face upward are observed.(a) What is the probability that the numbers add up to 8 ?(b) What is the probability that the sum of the numbers is less than 4 ?An experiment consists of tossing a coin two times and observing the sequence of heads and tails. Each of the four outcomes has the same probability of occurring.(a) What is the probability...
2. A fair red die and a fair blue die are rolled 2 times each. What is the probability of the product of numbers on the red die is less then the sum of numbers on the blue die? -Ive already posted this question but the answer given didn't explain how to calculate the number of successful cases. I know the total possible cases is 6*6*6*6=1296, but how do you calculate the number of successful cases?
Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,