Question

2. Two dice are thrown. a. What is the probability that a A w KI 4 appears on one die only KI b. What is the probability that at least one 4 appears? Ki c. What is the probability of rolling a sum of6 or doubles d. What are the odds against of rolling a pair, followed by two even K2 numbers in 2 consecutive rolls?

Answer 1

Two dice are thrown
The sample space is

11	21	31	41	51	61
12	22	32	42	52	62
13	23	33	43	53	63
14	24	34	44	54	64
15	25	35	45	55	65
16	26	36	46	56	66

N = total number of possibilities in 2 dice rolls = 36       
a) P(4 appears on one die only) = Number of favourable occurences / N       
   = 10/36      
   = 0.2778      
P(4 appears on one die only) = 0.2778       
        
b) P(atleast one 4 appears) = P(one 4 appears) +P(two 4s appear)       
   = 10/36 + 1/36      
   = 11/36      
   = 0.3056      
P(atleast one 4 appears) = 0.3056       
        
c) P(rolling a sum of 6 or doubles)       
We have following 11 possibilities for sum of 6 or doubles       
  15, 24, 33, 42, 51, 11, 22, 33, 44, 55, 66      
P(rolling a sum of 6 or doubles) = 11/36       
   = 0.3056      
P(rolling a sum of 6 or doubles) = 0.3056       
        
d) Odds against rolling a pair followed by 2 even numbers in 2 consecutive rolls       
Total combinations possible in 2 consecutive rolls = 6 x 6 x 6 x 6 = 1296       
Number of pairs = 6       
Number of occurences of 2 even numbers = 9     (22,24,26,42,44,46,62,64,66)  
Thus, number of scucesses = 6x9=54       
Number of failures = 1296 - 54 = 1242       
Odds against rolling a pair followed by 2 even numbers in 2 consecutive rolls = 1242 : 54