Multiple choice

A pair of dice is thrown $4$ times. If getting a double is considered a success, find the probability of two successes(approximately).

  1. $0.12$
  2. $0$
  3. $0.86$
  4. $1$
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A Correct answer
Explanation

Probability of success (double) p = 6/36 = 1/6. n = 4, k = 2. Binomial probability = C(4, 2) * (1/6)^2 * (5/6)^2 = 6 * (1/36) * (25/36) = 150/1296 approx 0.1157, which rounds to 0.12.

AI explanation

This is a binomial distribution where the probability of getting a doublet in a single throw of two dice is 6/36, which simplifies to 1/6. The probability of exactly two successes in four throws is found using the binomial probability formula: 4C2 times (1/6)^2 times (5/6)^2. Calculating this gives 6 times (1/36) times (25/36), which equals 150/1296, or approximately 0.12.

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