Probability of obtaining head and number 6:

- Coin Toss:
The first step in solving this problem is to determine the probability of obtaining a head on the first coin toss. Since the coin has two possible outcomes (head or tail) and each outcome is equally likely, the probability of obtaining a head is 1/2.

- Die Roll:
Next, we need to determine the probability of rolling a number 6 on a die. A standard die has six sides, numbered 1 to 6, and each side is equally likely to come up. Therefore, the probability of rolling a number 6 is 1/6.

- Conditional Probability:
Now that we have the individual probabilities, we need to calculate the conditional probability of obtaining a head and a number 6. In this case, the die is only rolled if a head comes up on the coin toss. So, the probability of obtaining a head and a number 6 is equal to the probability of obtaining a head multiplied by the probability of rolling a number 6 given that a head has come up.

P(head and 6) = P(head) * P(6 | head)

P(head and 6) = (1/2) * (1/6)

P(head and 6) = 1/12

- Coin Toss Again:
However, we also need to consider the possibility of obtaining a tail on the first coin toss. If a tail comes up, the coin is tossed again. In this case, we go through the same process of calculating the conditional probability.

P(tail) = 1/2

P(head on second toss) = 1/2

P(head and 6 | tail) = P(head on second toss) * P(6 | head on second toss)

P(head and 6 | tail) = (1/2) * (1/6)

P(head and 6 | tail) = 1/12

- Total Probability:
To find the total probability of obtaining a head and a number 6, we need to consider both possibilities: obtaining a head on the first toss or obtaining a tail on the first toss and then a head on the second toss.

P(head and 6) = P(head and 6 | head) * P(head) + P(head and 6 | tail) * P(tail)

P(head and 6) = (1/12) * (1/2) + (1/12) * (1/2)

P(head and 6) = 1/24 + 1/24

P(head and 6) = 2/24

P(head and 6) = 1/12

Therefore, the probability of obtaining a head and a number 6 is 1/12, which is equivalent to option 'A' (1/8) in the given answer choices.