Question

In: Advanced Math

. 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.

  1. What is the probability that you win this game?

Solutions

Expert Solution

Kindly give a thumbs up.


Related Solutions

A player pays $ 13 to roll three six-sided balanced dice. If the sum of the...
A player pays $ 13 to roll three six-sided balanced dice. If the sum of the 3 dice is less than 13, then the player will receive a prize of $ 70. Otherwise, you lose the $13. a. Find the expected value of profit.
Suppose you roll three fair six-sided dice and add up the numbers you get. What is...
Suppose you roll three fair six-sided dice and add up the numbers you get. What is the probability that the sum is at least 16?
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
Do the following code by using python: ( Thank!) You roll two six-sided dice, each with...
Do the following code by using python: ( Thank!) You roll two six-sided dice, each with faces containing one, two, three, four, five and six spots, respectively. When the dice come to rest, the sum of the spots on the two upward faces is calculated. • If the sum is 7 or 11 on the first roll, you win. • If the sum is 2, 3 or 12 on the first roll (called “Mygame”), you lose (i.e., the “house” wins)....
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
1. Rolling two D20 Consider what hapens when we roll two 20-sided dice d1 and d2...
1. Rolling two D20 Consider what hapens when we roll two 20-sided dice d1 and d2 (so the sample space is S={(d1,d2):d1,d2∈{1,2,3,…,20}} and Pr(ω)=1/|S| for each ω∈S). Consider the following events: A is the event "d1=13" B is the event "d1+d2=15" C is the event "d1+d2=21" Use the definitions of independence and conditional probability to answer these two questions: Are the events A and B independent? Are the events A and C independent?
You roll two 6-sided dice numbered 1 through 6. Let A be the event that the...
You roll two 6-sided dice numbered 1 through 6. Let A be the event that the first die shows the number 3, let B be the event that the second die shows a 5, and let E be the event that the sum of the two numbers showing is even. Compute P(A)and P(B)and then compute P(AlB). What does this tell you about events A and B?Hint: Remember that the sample space has 36 outcomes! Compute P(ElA)and compute P(E). What does...
Please using python to do the following code: You roll two six-sided dice, each with faces...
Please using python to do the following code: You roll two six-sided dice, each with faces containing one, two, three, four, five and six spots, respectively. When the dice come to rest, the sum of the spots on the two upward faces is calculated. • If the sum is 7 or 11 on the first roll, you win. • If the sum is 2, 3 or 12 on the first roll (called “Mygame”), you lose (i.e., the “house” wins). •...
Roll three (6-sided) dice. Let X denote the maximum of the values that appear. a. Find...
Roll three (6-sided) dice. Let X denote the maximum of the values that appear. a. Find P(X=1).?? b. Find P(X=2).?? c. Find P(X=3). d. Find P(X=4).?? e. Find P(X=5).? f. Find P(X=6). [Hint: It might be helpful to first find the values of P(X?x).]
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
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT