Noah N. answered • 12d

Experienced Tutor and ACT Certified Educator

Probability is always set up as a fraction with __favorable outcomes__ in the numerator (top) and total outcomes in the denominator (bottom). In this case we are being asked about rolling an **odd, prime** number on a 6-sided die. 1 is not a prime number, and although 2 is a prime number it is not odd, but *3 is an odd prime number*. Four is not odd nor is it prime, *but 5 is an odd prime number. *Six is again neither odd nor prime. Therefore, we have __two favorable outcomes__. There are six total outcomes of rolling each die, so our probability of rolling an odd, prime number is 2/6, which simplifies by dividing both numbers in the numerator and denominator by 2, to 1/3. Since we are being asked about rolling the die 3 times, and each roll is an independent event since the die has no memory of previous rolls, the probability of rolling an odd, prime number three times in a row is the product of multiplying the probabilities of each roll. Since each roll is the same and therefore has the same probability, the total probability is (1/3)(1/3)(1/3) = 1/27.