Consider a set of three standard six-sided dice (labelled with pips). What is the probability that...

Consider a set of three standard six-sided dice (labelled with pips). What is the probability that the total number of pips shown on three dice thrown at the same time is 11? (I.e., P(11) = ?) What is the probability that the total is 12? (I.e., P(12) = ?)

What is the fallacy in the following argument?

The number 11 occurs in six ways: (1,4,6), (2,3,6), (1,5,5), (2,4,5), (3,3,5), (3,4,4). The number 12 also occurs in six ways: (1,5,6), (2,4,6), (3,3,6), (2,5,5), (3,4,5), (4,4,4). Therefore the two numbers, 11 and 12, should be equally probable.

Expert Solution

Please upvote the solution.

Colby Messinger answered 2 years ago

. Three Dice of a Kind Consider the following game: You roll six 6-sided dice d1,…,d6...

. Three Dice of a Kind Consider the following game: You roll six 6-sided dice d1,…,d6 and you win if some number appears 3 or more times. For example, if you roll: (3,3,5,4,6,6) then you lose. If you roll (4,1,3,6,4,4) then you win. What is the probability that you win this game?

Two fair six sided dice are rolled. (i) What is the probability that the smaller value...

Two fair six sided dice are rolled. (i) What is the probability that the smaller value of the two results is 3 given that the sum of the two results is 8? (ii) What is the probability that the sum of the two results is at most 5 given that the number 2 appeared at least once? (iii) What is the probability that the sum of the two results is 7 given that exactly one of the two results is...

suppose that you are tossing two six sided dice one by one. What is the probability...

suppose that you are tossing two six sided dice one by one. What is the probability that (a) you will observe a total of 10? (b) You will observe a six on any dice? (c) You will observe a total at most of 7? (d) You will observe at least 11?

Two six-sided dice are rolled. (Enter your probabilities as fractions.) (a) What is the probability that...

Two six-sided dice are rolled. (Enter your probabilities as fractions.) (a) What is the probability that the sum of the numbers is greater than eight? Correct: 5/18 (b) What is the probability that the sum of the numbers is greater than eight, given that the first die is a 4??? (c) What is the probability that the first die shows a 4, given that the sum of the numbers is greater than eight???

7. Two fair six sided dice are rolled. (i) What is the probability that the sum...

7. Two fair six sided dice are rolled. (i) What is the probability that the sum of the two results is 6? (ii) What is the probability that the larger value of the two results is 4? (iii) What is the probability that the both results are at most 4? (iv) What is the probability that the number 3 appears at least once?

Consider a six-sided fair dice. Complete the following tables for this die: Number on the dice...

Consider a six-sided fair dice. Complete the following tables for this die: Number on the dice Number of times it appears on the dice Relative frequency of seeing that number 1 2 3 4 5 6 Total This is the entire question, does not say how many times the dice is thrown

Two ordinary fair, six-sided dice ate rolled. What is the probability the sum of the numbers...

Two ordinary fair, six-sided dice ate rolled. What is the probability the sum of the numbers on the two dice is 6, given that the number on at least one of the dice is 3? What is the probability the sum of the numbers on the two dice is 8, given that the number on at least one of the dice is 3? What is the probability that the sum of the numbers on the two dice is 9, given...

You roll two six-sided even dice. What is the probability that you get a score of...

You roll two six-sided even dice. What is the probability that you get a score of at least 11? a. 2/11 b. 1/12 c. 1/18 d. 1/6     You toss a fair coin 3 times in a row. What is the probability of getting at most two heads? a. 3/4 b. 1/4 c. 3/8 d. 7/8

You toss a pair of fair six-sided dice 30 times. What is... The probability that none...

You toss a pair of fair six-sided dice 30 times. What is... The probability that none of the 30 throws give a total of 12? The probability that a total of 7 appears 5 or more times?

If you roll two six-sided dice, what is the probability of obtaining the following outcomes? a)2...

If you roll two six-sided dice, what is the probability of obtaining the following outcomes? a)2 or 3 b) 6 and 4 c) At least one 5 d) Two of the same number (two 1s, or two 2s, or two 3s, etc.) e) An even number on both dice f) An even number on at least one die

Question