Multiple choice

A die is loaded in such a way that each odd number is twice as likely to occur as each even number . Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.

  1. $\dfrac{5}{9}$
  2. $\dfrac{4}{9}$
  3. $\dfrac{2}{9}$

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

Let p(even) = x, then p(odd) = 2x. Total probability: 3*x + 3*2x = 1, so 9x = 1, x = 1/9. Odds are 2/9, evens are 1/9. P(G) = P(4) + P(5) + P(6) = 1/9 + 2/9 + 1/9 = 4/9.

AI explanation

Let the probability of rolling an even number be x, making the probability of rolling an odd number 2x. The total probability is 3x + 3(2x) = 9x = 1, so x = 1/9. The event of rolling a number greater than 3 includes 4, 5, and 6, yielding probabilities of 1/9, 2/9, and 1/9 respectively. Adding these probabilities gives 1/9 + 2/9 + 1/9 = 4/9.

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