About A 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) The first flip comes up tails and there are at least two consecutive flips that come up heads.

a. 1/4

b. 1/2

c. 3/16

Step-by-step explanation:

The probability of an outcome, is the possibility of such outcome to occurs.

A. To find the probability of the first and last flip to be head will be;

, HHTH, HTHH, HTTH,

This are the only ways the first and last flip can be head. Therefore the probability is the number of possible ways divided by the total outcome;

4/16 = 1/4

B. To find the probability that atleast two consecutive flip comes out head. The possible ways this can happen are;

, HHHT, THHH, HHTH, HHTT, THHT, TTHH, HTHH.

Therefore the probability is the number of possible ways divided by the total outcome;

8/16 = 1/2

C. To find the probability that the first flip comes up tails and there are at least two consecutive flips that come up heads. The possible ways that this can happen are as follows;

THHH, THHT, TTHH.

Therefore the probability is the number of possible ways divided by the total outcome;

3/16

$30.32

step-by-step explanation:

65.00*.12=2.80

65.00-2.80=57.20

57.20*1.06=60.632

60.632/2=30.316