Question

Multiple choices Select the best answer. If I toss u fair coin five times and the outcomes are T'I"I"I'I, then the probability that tails appears on the next toss is (a) 0.5 (b) Less than 0.5 (c) greater than 0.5 . (e) $1 .$ (d) $0 .$

Name: Problem 32, Chapter 5: The Practice of Statistics for AP
Uploaded: 2023-01-16T16:15:37-08:00
Duration: 1 min 48 s
Channel: Jacob Fry
Description: Multiple choices Select the best answer. If I toss u fair coin five times and the outcomes are T'I"I"I'I, then the probability that tails appears on the next toss is (a) 0.5 (b) Less than 0.5 (c) greater than 0.5 . (e) 1 . (d) 0 .

   Multiple choices Select the best answer.
If I toss u fair coin five times and the outcomes are T'I"I"I'I, then the probability that tails appears on the next toss is
(a) 0.5
(b) Less than 0.5
(c) greater than 0.5 . (e) $1 .$
(d) $0 .$

The Practice of Statistics for AP

Daxen S.Starnes,… 4th Edition

Chapter 5, Problem 32

Instant Answer

Solved by Expert Jacob Fry

01/16/2023

Step 1

The problem asks for the probability of getting a tails (T) on the sixth toss of a fair coin, given that the first five tosses resulted in the sequence T, H, H, H, H. Show more…

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Multiple choices Select the best answer. If I toss u fair coin five times and the outcomes are T'I"I"I'I, then the probability that tails appears on the next toss is (a) 0.5 (b) Less than 0.5 (c) greater than 0.5 . (e) $1 .$ (d) $0 .$

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Key Concepts

Independence of Events

In probability theory, independent events are those where the outcome of one event does not affect the outcome of another. In a sequence of coin tosses, each toss is independent, meaning that what happened in previous tosses has no bearing on the outcome of the next toss.

Fair Coin

A fair coin is one that has an equal probability of landing on heads or tails, typically 0.5 for each outcome. This guarantees that every coin toss yields a heads or tails with equal likelihood, regardless of the outcomes of previous tosses.

Gambler's Fallacy

Gambler's Fallacy is the mistaken belief that a deviation from expected behavior in the short term will be corrected in the short term. In the context of coin tossing, it refers to the incorrect assumption that a series of similar results will influence the outcome of the next toss, despite the events being independent.

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