Question

ur the uennitionls dò hot match any of the terms. 2.3. Problem. Three fair, six-sided dice colored red, green and blue are rolled. Calculate each of the following probabilities:

Answer 1

Three fair six sided dice rolled.

Total ways =6*6*6=216

d) probability that sum of all three dice is exactly 10

Sum =10

(1,3,6) --->it can be done in 3*2*1= 6 ways

(1,4,5) ---> it can be done in 6 ways

(2,2,6) ---> it can be done in 6/2= 3 ways

(2,3,5) ---> it can be done in 6 ways

(2,4,4) .---> it can be done in 6/2= 3 ways

(3,3,4) ---> it can be done in 3 ways

Total =6+6+3+6+3+3=27 ways

Probability that sum is exactly 10 is 27/216 = 1/8

Probability=0.125

e) probability that sum is less than 10

Sum={3,4,5,6,7,8,9}

Sum=3 --> (1,1,1) --->1 way

Sum=4 --->(1,1,2) --->3 ways

Sum=5 ---->(1,1,3) (1,2,2) ---> 3+3= 6 ways

Sum=6 ---> (1,1,4) (1,2,3) (2,2,2) ---> 3+6+1=10 ways

Sum =7 ---> (1,1,5) (1,2,4) (1,3,3) (2,2,3) ---> 3+6+3+3 =15 ways

Sum=8 ---> (1,1,6) (1,2,5) (1,3,4) (2,2,4) (2,3,3)=3+6+6+3+3=21 ways

Sum=9 ---> (1,2,6) (1,3,5) (1,4,4) (2,2,5) (2,3,4) (3,3,3)= 6+6+3+3+6+1=25 ways

Total number of ways = 1+3+6+10+15+21+25=81

Probability= 81/216= 0.375

f) probability that sum is greater than 10

Probability= 1- p(sum less than equal to 10)= 1- 0.125-0.375

Probability= 1-0.5=0.5

Probability that sum is greater than 10 is 0.5