Discrete matha coin is flipped four times. for each of the events described below, express the event as a set in roster notation. each outcome is written as a string of length 4 from {h, t}, such as hhth. assuming the coin is a fair coin, give the probability of each event.( a ) the first and last flips come up heads.( b ) there are at least two consecutive flips that come up heads.( c) there are at least two consecutive flips that are the same

a) 25%

b) 50%

c) 87.5%

Step-by-step explanation:

There are number of outcome in total.

a)First and last flips come up heads. There are 4 outcomes here. Probability of the event is 4/16 = 1/4, or 25%.

- HHHH

- HHTH

- HTHH

- HTTH

b) at least 2 Consecutive flips that is heads. There are 8 outcomes. Probability of event is 8/16 = 1/2, or 50%

- HHHH

- HHHT

- HHTH

- HHTT

- THHH

- THHT

- HTHH

- TTHH

c) At least 2 consecutive flips that are the same. There are 14 outcomes. Probability of 14/16 = 7/8, or 87.5%

- HHHH

- HHHT

- HHTH

- HHTT

- THHH

- THHT

- HTHH

- TTHH

- TTTT

- TTTH

- TTHT

- HTTT

- HTTH

- THTT