Q 32. If I toss a fair coin five times... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 5: Q 32. (page 298)

If I toss a fair coin five times and the outcomes are $\{T T T T T\}$ , then the probability that tails appears on the next toss is (a) 0.5. (b) less than $0.5$ (c) greater than $0.5$ (d) $0$ (e) $1$ Exercises $33$ to $35$ refer to the following setting. A basketball player makes $47 %$ of her shots from the field during the season.

Short Answer

Expert verified

$2^{3}$ is the sum of all potential outcomes in any order.

Step by step solution

Step 1. Given Information

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

Step 2. Concept Used

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).

Step 3. Calculation

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. $2^{3}$ $\{H, T\}$ is the sample of a fair coin toss. $\{H H H H H, H H H H T, H H H T H, H H T H H, H T H H H, . . . . . . . . . . . T T T T T\}$ The probability of a tails result on the next flip is always equal to $0.5$ It makes no difference if previous outcomes were $\{T T T T T\}$ , $\{H H H H H\}$ or $T H T H T$ 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.