Question

a fair coin is tossed 28 times. in how many outcomes do at most 26 tails occur? a) 378 b) 268,435,427 c) 268,435,049 d) 29 e) 407 f) none of the above.

Answer 1

To find the number of outcomes in which at most 26 tails occur when a fair coin is tossed 28 times, we can use the concept of binomial coefficients.

Step-by-step explanation:

To find the number of outcomes in which at most 26 tails occur when a fair coin is tossed 28 times, we can use the concept of binomial coefficients. At most 26 tails occur means we can have 0, 1, 2, ..., 26 tails. The number of ways to choose k tails out of n tosses can be calculated using the formula:

C(n, k) = n! / (k!(n-k)!)

For k = 0, 1, 2, ..., 26, we need to calculate the sum of the binomial coefficients. Performing the calculations, we find:

Sum = C(28, 0) + C(28, 1) + C(28, 2) + ... + C(28, 26)

Sum = 378

Therefore, the answer is 378 (option a).

Answer 2

The number of outcomes with at most 26 tails when a fair coin is tossed 28 times is 2^28 minus the number of outcomes with 27 tails and 28 tails. To get the precise answer, one should use binomial coefficients or statistical software as the calculations involve large numbers.

Step-by-step explanation:

To determine how many outcomes result in at most 26 tails occurring when tossing a fair coin 28 times, we need to consider all the possible outcomes with 0 to 26 tails. This can be calculated using the binomial theorem or by referring to a binomial distribution table. However, for such calculations, computation tools or statistical software are typically used to handle these large numbers efficiently.

Since the total number of outcomes when tossing a fair coin 28 times is 228 (each toss has 2 possible outcomes), and we want the number of outcomes where there are at most 26 tails, we would sum the outcomes for 0 tails, 1 tail, ... up to 26 tails. This leaves out the scenarios where there are 27 or 28 tails, which are not part of the at most 26 criteria.

A calculation error would result if we did not subtract these two scenarios (27 and 28 tails), as we are looking for the number of outcomes with at most 26 tails. The answer to the question would be 228 minus the outcomes with 27 tails and minus the outcomes with 28 tails. However, without directly calculating or using the binomial coefficients for each case, we cannot identify the correct answer based on the options provided without further information.