Correct Answer - Option 1 : 193/792

**Calculation:**

⇒ Let us define the events

⇒ A : head appears.

⇒ B : Tail appears

⇒ C : 7 or 8 is noted.

⇒ We have to find the probability of C i.e. P (C)

⇒ P(C) = P(A) P (C/A) + P(B) P(C/B)

⇒ Now we calculate each of the constituents one by one

⇒ P(A) = probability of appearing head = 1/2

⇒ P(C/A) = Probability that event C takes place i.e. 7 or 8 being noted when head has already appeared. (If something has already happened then it becomes certain, i.e. now it is certain that head has appeared we have to certainly roll a pair of unbiased dice).

⇒11/36 (since (6, 1) (1, 6) (5, 2) (2, 5) (3, 4) (4, 3) (6, 2) (2, 6) (3, 5) (5, 3) (4, 4) i.e. 11 favourable cases and of course 6 × 6 = 36 total number of cases)

⇒ Similarly, P(B) = 1/2

⇒ P(B/C) = 2/11 (Two favourable cases (7 and 8) and 11 total number of cases).

⇒ Hence, P(C) = 1/2 × 11/36 + 1/2 × 2/11 = **193/792**