1. Two dices are thrown (a) List the elements of the sample space. (b) List the...
1. Roll a pair of dice, one red and one green. Now, define the following events: A is the event that at least one of the dice will be an even number B is the event that the sum of the die will be equal to 7; C is the event that at least one of the dice is equal to 1 (a) Draw a picture of the sample space. (b) List all the outcomes for each of the events...
QUESTION 7 Which of the two events are mutually exclusive? OA. Toss a coin to get a head or tail OB. Roll a die to get an even number or 4 OC. Roll two dices to get two even numbers or a sum of 8 D. Roll a die and get a prime number or 3 QUESTION 8 Probability of events must lie in limits of OA. 1-2 B. 2-3 OC.0-1 OD.-1-1 QUESTION9 Sample space (e.g. all possible outcomes) for...
1. Two dice are thrown. Let E be the event that the sum of the dice is odd, let F be the event that at least one of the dice lands on 1, and let G be the event that the sum is 5 . List the outcomes ina. E ∩ Fb. E ∪ Fc. E ∩ F'd. E ∩ F ∩ G
Please answer the questions clearly
1. Roll a pair of dice, one red and one green. Now, define the following events: A is the event that at least one of the dice will be an even number B is the event that the sum of the die will be equal to 7; C is the event that at least one of the dice is equal to 1 (a) Draw a picture of the sample space. (b) List all the outcomes...
1. You roll a pair of standard dice. Create the sample space for a single roll of the dice and use the sample space to compute the following probabilities. A. Create a sample space. B. P ( getting a 1 on the first die or getting a 5 on the second die) C. P (Sum of the dice = 10) D. P ( getting a 3 on the second die given that you got a 2 on the first die)...
Explain when will two events be independent and when will two events be mutually exclusive. Can two mutually exclusive events be independent also? Can two independent events be mutually exclusive? Suppose the experiment is roll two dice. Consider events E= both numbers are even. F = both numbers are odd, Are E and F mutually exclusive? Are they independent? Consider events U and V. U= the first number is even, V= the second number is even. Are U and V mutually...
Two coins are flipped and a die is rolled. (a) Write the sample space for this experiment. (b) Let A be the event that both coins will be heads. Write the outcomes in A. (c) Let B be the event that result of the dice roll will be an odd number. Write the outcomes in B.
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled twice. For example, "1,4" would indicate 1 was rolled first and then 4 was rolled second a) Write down the possible outcomes, i.e., the sample space. (b) List the outcomes in the following events: Event A: The number 4 came up zero times. Event B: The number 4 came up exactly one time. . Event C: The sum of the two rolls is odd...
Conditional Probability Two fair dice are rolled: (a) Express the sample space S in set builder notation and the probability P "At least one of the dice rolls a four." Write all possible outcomes of A (b) Consider the event A (c) What is the probability that at least one die rolls a four? (d) What is the conditional probability that the first die rolls a four given that the sum of the dice is six? (e) What is the...
Problem 2. (30 points) a) (5 points) In rolling 3 fair dice, what is the probability of obtaining a sum not greater than 77 b) (5 points) In rolling 2 fair dice, what is the probability of a sum greater than 3 but not exceeding 6? o) (5 points) Given that the frstroll was an odd number what is the probability that sum exceeds 6? The notation for this is P(A I B)- Probability(sum exceeds 6 given that the first...