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JEE Math Practice Question

A six faced die is biased such that $$3 \times \mathrm{P}($$a prime number$$)\,=6 \times \mathrm{P}($$a composite number$$)\,=2 \times \mathrm{P}(1)$$. Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

  1. A.$$\frac{3}{11}$$
  2. B.$$\frac{5}{11}$$
  3. C.$$\frac{7}{11}$$
  4. D.$$\frac{8}{11}$$

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