Answer: i) 12.5% ii) 87.5% iii) 23.4%
Step-by-step explanation:
There are two die, each with 8 sides so the total number of outcomes is 8²
i) Product is a prime number --> 2, 3, 5, 7
Since it is a prime we only have the option of one die being a 1 and the other being the prime number.
So possible successful outcomes is: (1, 2), (1, 3), (1, 5), (1, 7), (7, 1), (5, 1), (3, 1), and (2, 1) = 8 options.
[tex]\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{8}{8^2}=\dfrac{1}{8}=\large\boxed{12.5\%}[/tex]
ii) Not a perfect square. Let's find the probability that it IS a perfect square and subtract that value from the total (64).
Product IS a perfect square --> 1, 4, 9, 16, 25, 36, 49, 64
Possible successful outcomes of a perfect square: (1, 1) (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8) = 8 options.
Product is NOT a perfect square = 64 - 8 = 56 options
[tex]\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{56}{8^2}=\dfrac{7}{8}=\large\boxed{87.5\%}[/tex]
iii) Product is a multiple of 5 --> 5, 10, 15, 20, ,25, 30, 35, 40,
Possible successful outcomes of a multiple of 5: (1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (7,5), (8, 5), (5, 8), (5, 7), (5, 6), (5, 4), (5, 3), (5, 2), (5, 1) = 15 options
[tex]\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{15}{8^2}=\dfrac{15}{64}=\large\boxed{23.4\%}[/tex]
You are limited to 3 questions on Brainly so hopefully you can follow what I did to answer the last two questions (less than or equal to 21) and (divisible by 4 or 6). If not, please post this question again and state "Need iv and v only".
