Question

finding classical probabilities in exercises 41–46, a probability experiment consists of rolling a 12 - sided die numbered 1 to 12. find the probability of the event. 41. event a: rolling a 2 42. event b: rolling a 10 43. event c: rolling a number greater than 4 44. event d: rolling a number less than 8 45. event e: rolling a number divisible by 3 46. event f: rolling a number divisible by 5

Explanation:

Step1: Total outcomes of 12-sided die

Total outcomes = 12 (numbers 1-12)

Step2: Favorable outcomes for Event A

Favorable outcome: {2} → count = 1

Step3: Calculate probability for A

$P(A) = \frac{\text{Favorable}}{\text{Total}} = \frac{1}{12}$

Step4: Favorable outcomes for Event B

Favorable outcome: {10} → count =1

Step5: Calculate probability for B

$P(B) = \frac{1}{12}$

Step6: Favorable outcomes for Event C

Numbers >4: {5,6,...,12} → count=8

Step7: Calculate probability for C

$P(C) = \frac{8}{12} = \frac{2}{3}$

Step8: Favorable outcomes for Event D

Numbers <8: {1,...,7} → count=7

Step9: Calculate probability for D

$P(D) = \frac{7}{12}$

Step10: Favorable outcomes for Event E

Divisible by 3: {3,6,9,12} → count=4

Step11: Calculate probability for E

$P(E) = \frac{4}{12} = \frac{1}{3}$

Step12: Favorable outcomes for Event F

Divisible by5: {5,10} → count=2

Step13: Calculate probability for F

$P(F) = \frac{2}{12} = \frac{1}{6}$

Answer:

Event A: $\frac{1}{12}$
Event B: $\frac{1}{12}$
Event C: $\frac{2}{3}$
Event D: $\frac{7}{12}$
Event E: $\frac{1}{3}$
Event F: $\frac{1}{6}$