Answer:
a) 14.29% probability that they pick the same number.
b) 85.71% probability that they pick the different numbers.
Explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The outcomes in this problem is as follows:
(Student A Number, Student B Number)
(1,1), (2,1), (3,1), (4,1), (5,1), (6,1), (7,1)
(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2)
(1,3), (2,3), (3,3), (4,3), (5,3), (6,3), (7,3)
(1,4), (2,4), (3,4), (4,4), (5,4), (6,4), (7,4)
(1,5), (2,5), (3,5), (4,5), (5,5), (6,5), (7,5)
(1,6), (2,6), (3,6), (4,6), (5,6), (6,6), (7,6)
(1,7), (2,7), (3,7), (4,7), (5,7), (6,7), (7,7)
So there are 49 total outcomes.
(a) What is the probability that they pick the same number?
There are 7 possible outcomes in which they pick the same number:
(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7)
So there is a 7/49 = 0.1429 = 14.29% probability that they pick the same number
(b) What is the probability that they pick different numbers?
There are 49-7 = 42 possible outcomes in which they pick different numbers.
So there is a 42/49 = 0.8571 = 85.71% probability that they pick the different numbers.