Problema Solution
In an experiment, 3 numbers ranging from 2 to 10 are selected at random one at a time. The same number cannot be selected more than once. What is the probability that the 3 numbers will be consecutive and increasing?
Answer provided by our tutors
the number of triples that are consecutive and increasing is 7:
2 3 4, 3 4 5, 4 5 6, 5 6 7, 6 7 8, 7 8 9, 8 9 10
the total number of triples out of the 9 elements from the set {2, 3, 4, 5, 6, 7, 8, 9, 10} is:
C(9, 3) = 9!/((9 - 3)! 3!)
C(9, 3) = 9!/(6! 3!)
C(9, 3) = 7*8*9/2*3
C(9, 3) = 84
the probability is:
p = 7/84
p = 0.0833