We roll 2 dice and sum the numbers on the faces. a) What is the probability...
We roll 2 dice and sum the numbers on the faces.
a) What is the probability that we roll a 5?
b) What is the probability that we roll a 2 or a 3?
c) What is the probability that we roll at least a 10?
d) What is the probability that we roll at most a 5?
e) What is the probability that we roll an even sum?
f) What is the probability that we roll either an even sum, or a sum of at least 9?
Homework Answers
Number of outcomes when 2 dices are rolled = 36
(a) 5 = (2,3), (3,2), (1,4), (4,1)i. e. 4 ways
Required probability = 4/36 = 1/9
(b) 2 or 3 = (1,1)(1,2),(2,1) i. e 3 ways
Required probability = 3/36 = 1/12
(c) atleast 10 = (5,5),(4,6),(6,4),(5,6),(6,5),(6,6) i. e 6 ways
Required probability = 6/36 = 1/6
(d) atmost 5 = (1,1),(1,2),(2,1),(2,2),(1,3),(3,1)(2,3),(3,2),(1,4),(4,1) i. e 10 ways
Required probability = 10/36 = 5/18
(e) even sum (2,4,6,8,10,12) = (1,1), (2,2),(1,3),(3,1),(1,5),(5,1)(2,4),(4,2),(3,3)(3,5)(5,3),(4,4)(2,6),(6,2)(5,5)(4,6),(6,4)(6,6) i. e 18 ways
Required probability = 18/36 = 1/2
(f) even sum or sum of atleast 9 = all the outcomes of part (e) just include (9,11) = (4,5),(5,4)(3,6),(6,3),(5,6),(6,5) = 6 ways
Total number of ways = 18 + 6 = 24 ways
Required probability = 24/36 = 2/3
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