Four coins are tossed, what is the probability of obtaining head on the second tossed?

Each coin has 2 possible outcomes (Head or Tail). For four coins, the total number of outcomes is $2^4$.

$$\text{Total outcomes} = 2 \times 2 \times 2 \times 2 = 16$$

For the second toss to be a head, the outcome is fixed as 'H'. The other three tosses (first, third, and fourth) can be either a Head or a Tail.

• First toss: 2 possibilities (H or T)
• Second toss: 1 possibility (H)
• Third toss: 2 possibilities (H or T)
• Fourth toss: 2 possibilities (H or T)

$$\text{Favorable outcomes} = 2 \times 1 \times 2 \times 2 = 8$$

The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.

$$P(\text{Head on second toss}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ $$P(\text{Head on second toss}) = \frac{8}{16} = \frac{1}{2}$$

The probability of obtaining a head on the second toss is $\frac{1}{2}$.