Compute the probabilities of the following events: -rolling a 6 on a six sided dice -drawing...
Homework Answers
A) P(rolling a 6 on a six sided die) = 1/6
B) P(drawing a 2 or a diamond) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13
C) P(flipping a coin 3 times and getting 0 heads) = 1/8
D) P(flipping a coin 3 times and getting at least 1 heads) = 7/8
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Compute the probabilities of the following events:
-rolling a 6 on a six sided dice
-drawing...
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e....
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
1. Consider the experiment of rolling a pair of dice values showing on the dice. experiment...
1. Consider the experiment of rolling a pair of dice values showing on the dice. experiment of rolling a pair of dice. Suppose we are interested in the sum of face a. How many simple events are possible? b. List the sample space. c. What is the probability of obtaining a 7? d. What is the probability of obtaining a value of 9 or more? Because each roll has six possible even values (2.4,6,8,10,12) and five possible odd values (3,5,7,9,11),...
1. We roll two fair 6-sided dice. Compute the probabilities of the following events. (a) The...
1. We roll two fair 6-sided dice. Compute the probabilities of the following events. (a) The sum is at most 6. (b) The sum is more than 6. (c) The sum is at most 6 and at least one die is a 4. 2. Consider the letters a,b,c. Suppose we draw 2 of the letters at random (allowing for repetition). Assume order matters. That is, ab is not the same as ba: Let A : The 2 letters are distinct....
You flip a fair coin. On heads, you roll two six-sided dice. On tails, you roll...
You flip a fair coin. On heads, you roll two six-sided dice. On tails, you roll one six-sided dice. What is the chance that you roll a 4? (If you rolled two dice, rolling a 4 means the sum of the dice is 4) O 1 2 3 36 1 2 1 6 + + 1 4 36 1 6 2 2 1 36 + -10 2 . 4 36 + 4 6 2 2
Part A: Consider rolling two standard six-sided dice. How many possible ways (microstates) are there to...
Part A: Consider rolling two standard six-sided dice. How many possible ways (microstates) are there to make the sum of the two dice add to seven (macro state)? а. 6 b. 3 с. 1 d. 7 flip a coin. What are the chances that every Part B: Twenty people each simultaneously coin will come up heads? a. 9.5 x 10A-7 % b. 1.9 х 10^-4 % c. 9.5 x 10^-5 % d. 50 Part C: Twenty people each simultaneously flip...
Tim rolls two six-sided dice and flips a coin.
Tim rolls two six-sided dice and flips a coin.All of the following are possible outcomes, EXCEPT:Heads, 3,41. Tails, 62, 8, Heads5, 2 , Tails
A six-sided dice is rolled twice. Find the probability that the larger of the two rolls...
A six-sided dice is rolled twice. Find the probability that the larger of the two rolls was less than or equal to5 A fair coin is flipped 3 times. Find the probability that exactly 1 of the flips will turn up as heads.
Consider the procedure of rolling a pair of dice 6 times and let x be the...
Consider the procedure of rolling a pair of dice 6 times and let x be the random variable consisting of the number of times the sum of the results is 7. The following table describes the probability distribution of x. X P(X) 0 0.334898 1 ¿? 2 ¿? 3 0.053584 4 0.008038 5 0.000643 6 0.000021 a) Find the missing probabilities b) It would be unusual to roll a pair of dice six times and get at least three times...
1) Two dice are tossed once. Compute the following probabilities. a. The toss results in a...
1) Two dice are tossed once. Compute the following probabilities. a. The toss results in a sum of 9 or 6 b. The toss results in sum of 18. c. The sum is less than 7 and even. 3) T fr in se 2) Two cards are selected from a standard deck without replacement. Compute the following probabilities. 4) Th co co se The first and second cards are diamonds. The second card is a diamond given that the first...
(A) If you roll 3 six-sided dice, what is the probability of getting an overall score...
(A) If you roll 3 six-sided dice, what is the probability of getting an overall score of 8? (B) If you roll 3 six-sided dice 4 times, what is the probability of getting an overall score of 8 four times in a row? (C) If you roll 3 six-sided dice 2 times, what is the probability of getting an overall score of 8 on the first roll and an overall score of 3 on the second roll?
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
1. Consider the experiment of rolling a pair of dice values showing on the dice. experiment of rolling a pair of dice. Suppose we are interested in the sum of face a. How many simple events are possible? b. List the sample space. c. What is the probability of obtaining a 7? d. What is the probability of obtaining a value of 9 or more? Because each roll has six possible even values (2.4,6,8,10,12) and five possible odd values (3,5,7,9,11),...
You flip a fair coin. On heads, you roll two six-sided dice. On tails, you roll one six-sided dice. What is the chance that you roll a 4? (If you rolled two dice, rolling a 4 means the sum of the dice is 4) O 1 2 3 36 1 2 1 6 + + 1 4 36 1 6 2 2 1 36 + -10 2 . 4 36 + 4 6 2 2
Part A: Consider rolling two standard six-sided dice. How many possible ways (microstates) are there to make the sum of the two dice add to seven (macro state)? а. 6 b. 3 с. 1 d. 7 flip a coin. What are the chances that every Part B: Twenty people each simultaneously coin will come up heads? a. 9.5 x 10A-7 % b. 1.9 х 10^-4 % c. 9.5 x 10^-5 % d. 50 Part C: Twenty people each simultaneously flip...
A six-sided dice is rolled twice. Find the probability that the larger of the two rolls was less than or equal to5 A fair coin is flipped 3 times. Find the probability that exactly 1 of the flips will turn up as heads.
1) Two dice are tossed once. Compute the following probabilities. a. The toss results in a sum of 9 or 6 b. The toss results in sum of 18. c. The sum is less than 7 and even. 3) T fr in se 2) Two cards are selected from a standard deck without replacement. Compute the following probabilities. 4) Th co co se The first and second cards are diamonds. The second card is a diamond given that the first...
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