Question

4.44 Coin Tossing. When a dime is tossed four times, there are the following 16 possible outcomes. Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are

Answer 1

There are 16 possible outcomes when a dime is tossed four times.

Step-by-step explanation:

When tossing a dime four times, each toss has two possible outcomes: heads (H) or tails (T). Since there are four tosses, the total number of outcomes is found by multiplying the number of possibilities for each toss: 2 × 2 × 2 × 2 = 16. Each toss is independent of the others, so the total number of outcomes is the product of the individual possibilities for each toss.

To represent these outcomes, consider the example given: HTTH. This means the first toss is heads (H), the second toss is tails (T), the third toss is tails (T), and the fourth toss is heads (H). The sequence of H and T for each toss forms a unique combination, resulting in a total of 16 possible sequences.

In a more general sense, if you have n independent events, each with two possible outcomes, the total number of possible outcomes is
`2^n`. In this case, n is 4 (the number of tosses), so
`2^4`equals 16. Therefore, there are 16 possible outcomes when a dime is tossed four times. Each outcome is equally likely, assuming a fair coin, making the probability of any specific sequence 1/16.