Discrete MathA coin is flipped four times. For each of the events described below, express the event as a set in roster notation

Question

3 years ago

9

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

Mathematics

1 answer:

Vladimir79 [104] · Answer 1 · 2022-08-02T03:17:40+03:00

Answer:

a) 25%

b) 50%

c) 87.5%

Step-by-step explanation:

There are $2^4 = 16$ 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