Answer :
Using the Fundamental Counting Theorem, the measures are given as follows:
a) 3 ways to roll a multiple of 3 on each trial.
b) 243 ways to roll a multiple of 3 on all five trials.
c) 0.00243 probability of rolling a multiple of 3 on all five rolls.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The multiples of 3 between 1 and 10 are given as follows:
3, 6 and 9.
Hence three multiples, which is the number of ways to roll a multiple of 3 on each trial.
Hence, the number of ways to roll a multiple of 3 on all five trials is:
N = 3 x 3 x 3 x 3 x 3 = 3^5 = 243.
The total number of outcomes of the five trials is:
T = 10^5.
Then the probability of rolling a multiple of 3 on all five rolls is:
243/(10^5) = 0.00243.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751
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