Question

In an experiment, 3 numbers ranging from 3 to 6 are selected at random one at a time. The same number cannot selected more than once. What is the probability that the 3 numbers will be consecutive and increasing?

Answer 1

1/12.

Explanation:

The total number of ways to arrange the 3 numbers from the 4 options (3,4,5,6)

= 4P3 = 4!/(4-3)!

= 4×3×2×1/1

= 24 ways

We can only arrange the numbers that are consecutive and increasing in the following ways:

345 or 456 = 2 ways.

The probability that 3 numbers will be consecutive and increasing

= 2 ways/24 ways

= 1/12

Answer 2

the probability that the 3 numbers will be consecutive and increasing;

P = 1/12 or 8.33%

Explanation:

Number of possible selections that the 3 numbers will be consecutive and increasing N1;

3,4,5 or 4,5,6

N1 = 2

Total number of possible selections without picking a number twice Nt;

Nt = 4×3×2 = 24

the probability that the 3 numbers will be consecutive and increasing P = N1/Nt

P = 2/24 = 1/12

P = 1/12 or 8.33%