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Two students each use a random number generator to pick an integer between 1 and 7.

(a) What is the probability that they pick the same number?
(b) What is the probability that they pick different numbers?

User Ianmcook
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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.

User Istao
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