4. (10 Points) Consider the experiment of rolling two dice. The following table lists all possible outcomes as ordered pairs (number on first dice, number on second dice): (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (1,2) (2,2) (3,2) (4,2) (5,2) (6,2) (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) (1,4) (2,4) (3,4) (4,4) (5,4) (6,4) (1,5) (2,5) (3,5) (4,5) (5,5) (6,5) (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) a. (5 Points) Find the probability that the sum of the numbers on the two dice is less than or equal to 5. P(Sum ? 5) = __________ b. (5 Points) Find the probability that the sum of the numbers on the two dice is even. P(Sum is even) = __________
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** Each die has 6 faces, so when rolling two dice, the total number of outcomes is \(6 \times 6 = 36\). Show more…
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Two six-sided dice are tossed. The sample space is given below. Round all answers to 3 decimal places. 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6 (a) What is the probability of rolling a 3 on either dice? (b) What is the probability of rolling a 5 and 7? (c) What is the probability of rolling a 2 and an odd number (in either order)? (d) What is the probability of rolling two numbers whose sum is odd or a multiple of 3?
Adi S.
Suppose you roll a pair of six-sided dice and add their totals. The probability model is given below: Sum | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 Probability | 1/36 | 1/18 | 1/12 | 1/9 | 5/36 | 1/6 | 5/36 | 1/9 | 1/12 | 1/18 | 1/36 (a) What is the probability that the sum of the numbers on your dice is 4 or 5? (b) What is the probability that the sum of the numbers on your dice is an even number or a number less than 6? (c) What is the probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
Steven C.
Roll 2 6-sided dice and record the sum (an online dice roller may be used) 1. Are these data discrete or continuous? (2 points) 2. List the sample space (hint: imagine the dice are different colors so you can tell the difference between them). (6 points) 3. What is the theoretical probability of getting a sum of 7 with 2 dice? (4 points) 4. Record the number of 7's rolled after: (3 points - 1 each) a. 10 rolls b. 25 rolls c. 50 rolls 5. Calculate the empirical probability of getting a sum of 7 with 2 dice after: (6 points - 2 each) a. 10 rolls b. 25 rolls c. 50 rolls 6. Which of these three numbers of rolls is closest to the theoretical probability? Does this make sense? Why? (4 points) 7. Is this a binomial probability model? How do you know? (4 points) 8. Create a probability density function table. (5 points) 9. Calculate the probability of rolling a sum of 7 (round answers to three decimal places): (6 points - 2 each) a. Exactly 4 out of 10 times b. At least 5 out of 25 times c. No more than 10 out of 50 times
Jesse Y.
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