Question

3. A fair coin is thrown once; if it lands heads up, it is thrown a second time. Find the frequency function of the total number of heads.

Answer 1

To determine the frequency function for the total number of heads when a fair coin is tossed, one must account for all possible outcomes. The probability for getting 0 heads is 0.5, for 1 head is 0.25, and for 2 heads is 0.25.

Step-by-step explanation:

In this scenario, we have a sequence of coin tosses where a fair coin is thrown once and, if it lands heads up, it is thrown a second time. To find the frequency function of the total number of heads, we need to consider all possible outcomes and their probabilities.

There are three possible outcomes when the coin is thrown:

1. The coin lands heads on the first throw (probability 0.5), and it is thrown again. There is a 50% chance it will land heads again and a 50% chance it will land tails.
2. The coin lands tails on the first throw (probability 0.5), and the process ends with zero heads.

The frequency function for the total number of heads (let's denote it as X) can be summarized as:

• P(X = 0) - The coin lands tails on the first throw: 0.5.
• P(X = 1) - The coin lands heads on the first throw and tails on the second: 0.5 * 0.5 = 0.25.
• P(X = 2) - The coin lands heads on both throws: 0.5 * 0.5 = 0.25.

The frequency function for the total number of heads therefore is:

• 0 heads (P(X = 0)) = 0.5
• 1 head (P(X = 1)) = 0.25
• 2 heads (P(X = 2)) = 0.25

Answer 2

The frequency function of the total number of heads when a fair coin is thrown is 0.25 for 0 heads, 0.5 for 1 head, and 0.25 for 2 heads.

Step-by-step explanation:

To find the frequency function of the total number of heads when a fair coin is thrown, we can consider the possible outcomes. If the coin lands heads up on the first throw, it is thrown a second time. This means there can be 0, 1, or 2 heads in total. Let's calculate the probability of each outcome:

1. If there are 0 heads, it means both throws landed tails. The probability is (0.5) * (0.5) = 0.25.
2. If there is 1 head, it means one throw landed heads and the other landed tails. There are two scenarios for this outcome: heads followed by tails or tails followed by heads. The probability is (0.5) * (0.5) + (0.5) * (0.5) = 0.5.
3. If there are 2 heads, it means both throws landed heads. The probability is (0.5) * (0.5) = 0.25.

The frequency function represents the probabilities assigned to each outcome. Therefore, the frequency function of the total number of heads is 0.25 for 0 heads, 0.5 for 1 head, and 0.25 for 2 heads.