Lets say were playing game with five dice The game consists

Let\'s say we\'re playing game with five dice. The game consists of three rounds. The object of the game is to roll all of the same number in those three rounds with all five dice.

EXAMPLE:

Let\'s say in Round 1 you roll a 3,5,6,1,3. You can do one of two things. You can remove any matching pair, in this case the two threes, or you can remove a single dice that does not have a matching pair, in this case the 5,6, or 1. In our case, we will remove both threes. Three is now called THE DESIGNATED NUMBER. Now we are left with three dice. We roll again for round two. This time we end up with 6,3,5. Because three is our designated number we keep the three that we rolled in this second round. We are left with two dice for the final round. We roll both dice. They end up being two threes. As you can see we now have five dice that have rolled all three\'s and therefore won the game.

MY QUESTION:

Let\'s say for the first round I roll a 1,2,3,4,5. Should I put aside one dice and make it\'s value my designated number and try to get the rest of the dice to match in rounds two and three? Or should I restart the game? Which scenario would have the highest probability of winning. Please show work.

Solution

The first round i roo is 1,2,3,4,5. I should put aside one dice and make its value mu designated number. Here if we choose 2 as a designated number. We have left is four dice, In the second number the number comes is 1,2,5,6. In the third round the the number comes is 5,3,2. So, we came 2 three same number in five dice but the designated number is a pair that is its two pair, three pair etc. When we use three, four and five same number then we getting three same number in the first round we donot paly the second and third round and these times the probability is low. The giving example is the highest probability when all numbers in the first round is different.