Multiple choice

A pair of dice is thrown simultaneously. Find the probability of getting $(i)$ a multiple of $3$ on both dice. $(ii)$ Sum of the numbers on two dice is always less than $7$. $(iii)$ An odd number on the first die and a prime number on the other.

  1. $(i)\quad \displaystyle\frac{1}{5} \\ (ii)\quad \displaystyle\frac{7}{13} \\ (iii)\quad \displaystyle\frac{1}{3}$
  2. $(i)\quad \displaystyle\frac{1}{7} \\ (ii)\quad \displaystyle\frac{11}{18} \\ (iii)\quad \displaystyle\frac{1}{7}$
  3. $(i)\quad \displaystyle\frac{1}{9} \\ (ii)\quad \displaystyle\frac{1}{12} \\ (iii)\quad \displaystyle\frac{1}{4}$

  4. None of these
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D Correct answer
AI explanation

For two dice, the probability of getting a multiple of 3 on both is 3 multiplied by 3 favorable outcomes out of 36, which is 9 divided by 36, or 1 divided by 4. The probability that their sum is less than 7 is 15 divided by 36, or 5 divided by 12. The probability of an odd number on the first die and a prime number on the second is 9 divided by 36, or 1 divided by 4. Since these values are not listed in the first three options, the correct choice is none of these.

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