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The outcome of $5$coin tossed $\left\{TTTTT\right\}$ On the following toss, we must determine the probability that tails will appear:

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$(never happens) and $1$(happens frequently) (always occurs).

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation. A sequence of five fair coin flips has a sample space that contains all potential outcomes. $2^3$$\left\{H,T\right\}$is the sample of a fair coin toss. $\left\{HHHHH,HHHHT,HHHTH,HHTHH,HTHHH,...........TTTTT\right\}$The probability of a tails result on the next flip is always equal to $0.5$It makes no difference if previous outcomes were $\left\{TTTTT\right\}$, $\left\{HHHHH\right\}$or $THTHT$ In each of these and all other circumstances, the probability of the next being tails is still $0.5$As a result, option (a) is correct.