Question

# You and a friend are rolling a set of 6 dice. The game works such that...

You and a friend are rolling a set of 6 dice. The game works such that if a die shows the values 1, 2, or 3 you will get a point for that die. Each die that shows 4, 5, or 6 your friend will get a point for.
Construct a probability model for a single roll of the dice then answer the following.

Step 1 of 5:

What is the probability you made 2 points?

Step 2 of 5:

What is the probability that your friend will score 2 points?

Step 3 of 5:

What is the probability you score 4 or more points in this round

Step 4 of 5:

If we play a second round of this game, what is the probability that you will have exactly 6 points at the end of the second round? [In this situation there have been a total of 12 dice rolled]

Step 5 of 5:

If we play another round [a total of 18 dice rolled] what is the probability you will have 10 or more points?

Step 1 of 5: as probability of a point on single die =1/2 (as there are 3 outcome to get a point out of 6)

probability you made 2 points =6C2(1/2)3(1/2)4 =0.234375

Step 2 of 5: probability that your friend will score 2 points =6C2(1/2)3(1/2)4 =0.234375
Step 3 of 5: probability you score 4 or more points in this round =P(X>=4)=P(X=4)+P(X=5)+P(X=6)

=6C4(1/2)4(1/2)2 +6C5(1/2)5(1/2)1 +6C6(1/2)6(1/2)0 =0.343750

Step 4 of 5: P(X=6)=12C6(1/2)6(1/2)6 =0.225586

Step 5 of 5:

P(X>=10)= =0.407265

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