In an experiment, a fair coin is tossed 13 times and the face that appears (H for head or T for tail) for each toss is recorded.

How many elements of the sample space will have no tails?
How many elements of the sample space will have exactly one tail?
How many elements of the sample space will start and end with different faces and have a total of exactly two tails?
How many elements of the sample space will start or end with a tail and have an adjacent pair or triple of tails and include a total of exactly three tails?

1) 1 element

2) 13 elements

3) 22 elements

4) 40 elements

Step-by-step explanation:

1) Only one element will have no tails: the event that all the coins are heads.

2) 13 elements will have exactly one tile. Basically you have one element in each position that you can put a tail in.

3) There are elements that have exactly 2 tails. From those elements we have to remove the only element that starts and ends with a tail and in the middle it has heads only and the elements that starts and ends with a head and in the 11 remaining coins there are exactly 2 tails. For the last case, there are possibilities, thus, the total amount of elements with one tile in the border and another one in the middle is 78-55-1 = 22

4) We can have:

For the first possibility there are 2 * 11 = 22 possibilities (first decide if the pair starts or ends and then select the remaining tail)

For the second possibility, we have 2*9 = 18 possibilities (first, select if there is a tail at the end or at the start, then put a head next to it and on the other extreme, for the remaining 10 coins, there are 9 possibilities to select 2 cosecutive ones to be tails).

This gives us a total of 18+22 = 40 possibilities.

146%

step-by-step explanation:

1696 hundred thousand

step-by-step explanation: