In a series of coin tosses, what is the probability that exactly four tosses are needed to get two heads?

In a series of coin tosses, what is the probability that exactly four tosses are needed to get two heads?

• A. 1/8
• B. 1/16
• C. 3/16
• D. 1/4

Answer: (C)

To determine the probability that exactly four tosses are needed to get two heads, we need to analyze the situation carefully. We want the second head to occur precisely on the fourth toss, which implies that within the first three tosses, there must be exactly one head. The outcomes for the first three tosses can be represented using the following possible scenarios: 1. H (Head), T (Tail), T (Tail) 2. T (Tail), H (Head), T (Tail) 3. T (Tail), T (Tail), H (Head) Each of these scenarios represents getting one head and two tails, and the fourth toss must be a head (H) to satisfy the condition of getting a second head on the fourth toss. Now, let's consider the arrangement and the calculation: - The specific arrangement of heads (H) and tails (T) in the first three tosses must result in one head and two tails. The probability of each specific arrangement (like H, T, T) occurring is given by the multiplication of the probabilities of individual tosses: P(H) * P(T) * P(T) = (1/2) * (1/2) * (1/2) = 1/

To determine the probability that exactly four tosses are needed to get two heads, we need to analyze the situation carefully. We want the second head to occur precisely on the fourth toss, which implies that within the first three tosses, there must be exactly one head.

The outcomes for the first three tosses can be represented using the following possible scenarios:

1. H (Head), T (Tail), T (Tail)

2. T (Tail), H (Head), T (Tail)

3. T (Tail), T (Tail), H (Head)

Each of these scenarios represents getting one head and two tails, and the fourth toss must be a head (H) to satisfy the condition of getting a second head on the fourth toss.

Now, let's consider the arrangement and the calculation:

• The specific arrangement of heads (H) and tails (T) in the first three tosses must result in one head and two tails. The probability of each specific arrangement (like H, T, T) occurring is given by the multiplication of the probabilities of individual tosses: P(H) * P(T) * P(T) = (1/2) * (1/2) * (1/2) = 1/