Question

If five numbers are selected at random from the set {1,2,3,...,20}, what is the probability that their minimum is larger than 5? (A number can be chosen more than once, and the order in which you select the numbers matters)

Answer 1

Answer:

the probability that their minimum is larger than 5 is 0.2373

Step-by-step explanation:

For calculate the probability we need to make a división between the total ways to selected the 5 numbers and the ways to select the five numbers in which every number is larger than 5.

So the number of possibilities to select 5 numbers from 20 is:

20                 *      20         *          20     *        20         *       20

First number  2nd number   3rd number  4th number   5th number

Taking into account that a number can be chosen more than once, and the order in which you select the numbers matters, for every position we have 20 options so, there are  $20^{5}$ ways to select 5 numbers.

Then the number of possibilities in which their minimum number is larger than 5 is calculate as:

15                 *      15         *             15     *        15          *       15

First number  2nd number   3rd number  4th number   5th number

This time for every option we can choose number from 6 to 20, so we have 15 numbers for every option and the total ways that satisfy the condition are  $15^{5}$

So the probability P can be calculate as:

$P=\frac{15^{5} }{20^{5} } \\P=0.2373$

Then the probability that their minimum is larger than 5 is 0.2373