Twenty-three coins are tossed; in how many ways can you have at least two tails?
To find the number of ways to have at least two tails when tossing twenty-three coins, we can use the concept of combinatorics.
First, let's determine the total number of possible outcomes when tossing twenty-three coins. For each coin, there are two possible outcomes: heads or tails. Since there are twenty-three coins, the total number of outcomes is 2 × 2 × 2 × ... (twenty-three times) = 2^23.
Next, we need to find the number of ways to have zero tails and one tail. The probability of getting zero tails (all heads) is (1/2)^23. The probability of getting one tail is (23/23) × (1/2) × (1/2)^22.
To find the number of ways to have at least two tails, we subtract the number of ways to have zero tails and one tail from the total number of possible outcomes:
Number of ways to have at least two tails = Total number of outcomes - Number of ways to have zero tails - Number of ways to have one tail.
Number of ways to have at least two tails = 2^23 - (1/2)^23 - (23/23) × (1/2) × (1/2)^22.
Simplifying this equation will give you the final answer.