Multiple choice

A dice is so biased that it is twice as likely to show an even number as an odd number when rolled. It is rolled twice. Find the probability that the sum of two numbers rolled is even.

  1. 4/9

  2. 5/9

  3. 2/3

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P(odd) = p, P(even) = 2p. p + 2p = 1 => p = 1/3. P(odd) = 1/3, P(even) = 2/3. Sum is even if both are odd or both are even. P(even sum) = P(O,O) + P(E,E) = (1/3 * 1/3) + (2/3 * 2/3) = 1/9 + 4/9 = 5/9.

AI explanation

Let the probability of an odd number be p and the probability of an even number be 2p. Since these are the only possible outcomes, p plus 2p equals 1, meaning p is 1/3 and the probability of an even number is 2/3. For the sum of two rolls to be even, the numbers must be both even or both odd. The probability of an even sum is the sum of their individual probabilities: (2/3 multiplied by 2/3) plus (1/3 multiplied by 1/3). This equals 4/9 plus 1/9, resulting in 5/9.

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