Question

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?

Answer 1

Answer:

• 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