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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?

Respuesta :

Edufirst

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

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