Question

A die has its six faces marked 0,1,1,1,6,6.
Two such dice are thrown together and the total score is recorded.
a)_ How many different scores are possible ?
b) What is the probability of getting a total of 7 ?

Answer 1

Hey there,

Lets first figure out how many different scores are possible as a combination of both dices are thrown - 
(0,0) = 0
(0,1) = 1
(0,6) = 6
(1,1) = 2
(1,6) = 7
(6,6) = 12

To get a score of 7, one dice must show 1 and one dice must show 6. 
Probability of dice getting 1 = 3/6 = 1/2. 
Probability of dice getting 6 = 2/6 = 1/3. 

Thus probability of getting score 7 is = 
1/2 * 1/3 + 1/2*1/3 = 1/3. 

Hope this helps!

Answer 2

Answer:

Step-by-step explanation:

since the dice has six faces marked as 0,1,1,1,6,6.

if two dice are thrown:

the different scores are {(0,0),(0,1),(0,6),(1,1),(1,6),(6,6)}i.e. {0,1,6,2,7,12}

total number of different scores are 6.

when one dice is thrown

the probability of getting 0 = 1/6

the probability of getting 1 = 3/6 =1/2

the probability of getting 6 = 2/6 = 1/3

to get a total of 7 , one dice must show 1 and other dice must show 6.

(1,6) or (6,1)

the required probability =

1/2×1/3+1/2×1/3=1/3.

hope this helps you.