A standard number cube numbered one through six on each side is rolled five times. What is the probability of landing on a three or four on all five rules?

1/243 ≈ 0.004 (which is a low probability)

Explanation:

The event landing on a three or four on a rolling is independent of the event of landing on a three or four on any other rolling.

Thus, for independent events you calculate the joint probability as the product of the probabilities of each event:

P (A and B and C and D and E) = P (A) * P (B) * P (C) * P (D) * P (E)

Here, P (A) = P (B) = P (C) = P (D) = P (E) = probability of landing on a three or four.

Now to calculate the probability of landing on a three or four, you follow this reasoning:

Positive outcomes = three or four Number of positive outcomes = 2 Possible outcomes = one, two, three, four, five, or six Number of possible outcomes = 6 Probability = numer of positive outcomes / numer of possible outcomes Probability = 2/6 = 1/3

Finally, probability of landing on a three or four on all five rolls: (1/3) ⁵ = 1/243 ≈ 0.004 ← answer