Answer:
Explanation:
A set of random numbers can be used for simulating a situation by defining how the numbers will be used to represent the possible outcomes. Trials are repeated using newly-generated random numbers until there are a sufficient number of trials to give a reasonable prediction of the probability of interest.
__
We can simulate the situation as follows:
- if a pair of digits is in the range 00-44, then the student will be taking a computer course
- a sequence of 10 pairs of digits (4 of the 5-digit numbers) will represent a group of 10 students
- We are interested in the fraction of groups of 10 that have 6 or more that take a computer course. (Theoretical probability is about 26%.)
Here are our trials and results.
48 09 52 47 65 05 60 44 64 97 -- 3 of 10
11 96 69 33 54 86 43 13 47 31 -- 5 of 10
56 52 16 97 22 26 29 57 94 23 -- 5 of 10
42 66 97 09 62 17 35 52 98 26 -- 5 of 10
53 44 26 82 41 88 38 32 64 31 -- 6 of 10
73 43 45 30 41 29 59 15 81 66 -- 5 of 10
23 54 46 11 32 12 95 52 28 34 -- 6 of 10
41 59 26 41 19 53 14 73 32 05 -- 7 of 10
82 87 37 09 67 70 03 44 78 21 -- 5 of 10
11 15 30 29 89 37 97 79 34 25 -- 7 of 10
__
Of these 10 trials, 4 showed the result that at least 6 of the next 10 students will choose a computer course. That is, the probability is estimated to be about 4/10 = 40%.
_____
Additional comment
Here, we can only predict the probability of interest as some multiple of 10%, since we have numbers sufficient for only 10 trials.
We could arrange the random numbers a different way and reuse them, but we choose not to for the purpose of this answer. For that to make sense, we need to have assurance that these numbers are truly random.
The number of repeated values among these 100 pairs of digits suggests that this is a poor set of numbers to be using. 26 and 41 each show up 4 times, for example. The probability of that happening by chance in a truly random set of numbers is about 0.03%. A chance event is considered to be unlikely if its probability is less than 1%.