Question

Shen throws 2 dice and adds the numbers together.

a) What is the most likely possible total? b) what is the least likely possible total?

find the probability that the total will be:
c)2 d)7 e) less than 7 f) an odd number g) a prime number

Answer 1

total possible outcome are = (1,1) (1,2) (1,3) .......................(6,6)        (total 36
a) most likely possible total = 6+6 = 12
b) least likely possible total = 1+1 = 2
c) probability of getting total 2 = 1/36
d) total 7 = (1,6) (6,1) (2,5) (5,2) (3,4) (4,3) = 6
probability = 6/36 = 1/6
e) total less than 7 = 2,3,4,5,6 = (1,1) (1,2) (1,3) (1,4) (1,5) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (4,1) (4,2) = 14
 probability = 14/36 = 7/18
f) total will be an odd number only when one dice contain odd another contain even
(1,2) (1,4) (1,4) (3,2) (3,4) (3,6) (5,2) (5,4) (5,6) (2,1) (2,3) (2,5) (4,1) (4,3) (4,5) (6,1) (6,3) (6,5) 
 so total possible out come = 18
probability = 18/36 = 1/2
g) a prime number from 2 to 12 = 2,3,5,7,11
total getting 2 = (1,1)
total getting 3 = (1,2) (2,1)
total getting 5 = (1,4) (2,3) (3,2) (4,1)
total getting 7 = (1,6) (6,1) (2,5) (5,2) (3,4) (4,3)
total getting 11 = (5,6) (6,5)
probability = 15/36 = 5/12